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LOGIC 


OR  THE 
ANALYTIC  OF  EXPLICIT  REASONING 


BY 

GEORGE  H.  SMITH 

AUTHOR  OK  "ELEMENTS  OF  RIGHT  AND  OF  THE  LAW,"  "A  CRITICAL 

HISTORY  OF  MODERN  ENGLISH  JURISPRUDENCE,"  "THEORY 

OF  THE  STATE,"  AND  OTHER  WORKS 


i3331 

'QtNAM'S  S 


G.  P.  PUTNAM'S  SONS 
NEW  YORK  AND  LONDON 
fnucfcerbocfcer  prees 
1901 


COPYRIGHT,  1901 

BY 

GEORGE  H.  SMITH 


Che  Ytnicherbocfcer  press,  flew 


v    PREFACE 

IT  is  well  known  to  those  conversant  with 
the  current  literature  of  Logic  that  recent 
logical  theories  diverge  widely  from  the  old 
Logic  of  Aristotle  and  the  Schoolmen,  and  no 
less  widely  from  each  other.  From  this  it  hap- 
pens that,  under  the  common  name  of  Logic, 
we  have  many  doctrines  essentially  different 
from  each  other  ;  and  the  student  who  desires 
to  enter  upon  the  study  of  the  subject  is  thus 
confronted  with  the  preliminary  problem  of 
determining  under  what  name  the  true  Logic 
is  to  be  found.  Nor  in  this  case  can  he  expect 
much  help  from  his  instructors;  who,  like  the 
rest  of  the  logicians,  are  hopelessly  at  a  loss. 
Whether  he  shall  study  Logic — whatever  may 
be  his  wishes  and  his  determination — must 
therefore  be  a  matter  for  chance  to  determine. 
And,  even  should  he  be  so  lucky  as  to  light 
on  a  place  where  something  like  Logic  is 
taught,  it  will  probably  be  taught  in  so  muti- 
lated a  form  and  so  mingled  with  extraneous, 
and  even  inconsistent  matter,  that  it  will  be 


IV  PREFACE 

impossible  for  him  to  understand  it  or  to  ap- 
preciate its  utility.  Hence,  if  the  plain  truth 
is  to  be  told,  Logic,  in  the  true  sense  of  the 
term,  is  no  longer  taught  or  learned  anywhere; 
but  has  become  a  lost  art. 

But  while  the  logicians  of  the  day  are  thus 
at  variance  among  themselves,  there  is  un- 
fortunately one  point  in  which  they  agree 
with  each  other,  and  also  with  Whately  and 
others  of  the  older  logicians.  This  consists  in 
the  opinion  that  Logic  is  a  purely  formal 
science,  and  as  such  concerned  only  with  the 
forms,  and  not  with  the  matter  or  content  of 
language  or  of  thought;  or,  in  other  words, 
that  it  does  not  deal  with  what  is  thought  or 
expressed,  but  with  the  forms  of  the  thought 
or  expression  only.  From  this  it  must  follow — 
if  the  view  be  accepted  —  that  Logic,  except 
merely  as  an  improving  mental  exercise,  can 
be  of  no  practical  utility;  and  this  indeed  is 
commonly  asserted  and  always  implied  in  the 
Logics  of  the  day;  which,  though  essentially 
different  in  other  respects,  agree  in  this.  And 
from  this  again  it  must  follow — as  on  this  view 
was  irresistibly  argued  by  Locke,  Stewart, 
Reid,  and  others — that  the  subject  is  unworthy 
of  the  serious  attention  of  rational  men  ;  which, 
on  the  premises  assumed,  has  indeed  come  to 
be  the  verdict  of  the  common  sense  of  man- 
kind. Thus  the  student  is  discouraged  from 


PREFACE  V 

the  study  of  the  subject  not  only  by  the  con- 
fusion reigning  over  it  and  the  almost  insur- 
mountable initial  difficulty  of  recognizing  the 
true  Logic  among  so  many  pretenders,  but 
by  the  conviction  impressed  upon  him  by  an 
irresistible  argument  and  by  the  practically 
unanimous  teachings  of  logicians,  that  Logic 
cannot  be  put  to  any  practical  use. 

The  view  taken  of  Logic  in  this  work  is  dif- 
ferent. It  is  what  I  conceive  to  be  the  ancient 
and  orthodox  view,  that  Logic  has  to  deal  with 
the  matter  as  with  the  forms  of  thought  and  its 
expression  ;  that  it  embraces  in  its  scope  every- 
thing that  touches  the  right  use  of  words,  as 
instruments  of  reasoning,  or,  in  other  words, 
the  whole  subject  of  explicit  reasoning  or  ratio- 
cination ;  that  it  is  the  science  fundamental  to 
all  others  and  essential  to  all  who,  in  the  search 
after  truth,  would  pass  beyond  the  mere  evi- 
dence of  their  senses;  that,  in  its  educational 
aspect,  it  is  not  only  an  essential  part,  but  the 
very  foundation  of  rational  education ;  and 
finally  that,  in  use,  it  is  indispensable  to  the 
rectitude  of  thought  and  of  life.  Hence,  of 
all  branches  of  learning,  I  believe  it  to  be  of 
the  largest  practical  utility  to  man,  and  that 
all  the  learning  of  the  day  cannot  compen- 
sate for  its  loss;  and  also  that  its  decadence 
in  modern  times  has  been  one  of  the  great 
calamities  of  mankind.  All  this  I  attempt  to 


vi  PREFA  CE 

establish  and  to  illustrate  practically  in  the 
following  pages;  to  which  I  must  refer  for 
the  complete  proofs;  but  perhaps  something 
towards  this  end  may  be  effected  in  advance 
by  explaining  briefly  how  the  work  came  to  be 
written. 

In  the  investigation  of  Jurisprudence,  Poli- 
tics, and  Morality  generally  —  to  which  my 
studies  have  been  principally  devoted  —  two 
important  facts  were  forced  on  my  attention, 
that  seem  to  establish  my  present  thesis: 

(i)  The  first  of  these  was  that  the  prevailing 
errors  in  the  theory  of  Politics,  Sociology,  and 
Morality,  and  the  Moral  Sciences,  or  Science 
of  Human  Nature,  generally,  have  their 
sources,  almost  always,  in  merely  logical  fal- 
lacies, and  may  be  readily  refuted  by  the  ap- 
plication of  familiar  logical  principles;  all  of 
which  will  be  practically  illustrated  in  treating 
of  the  fallacies.  Here,  then,  I  think,  we  have 
a  practical  proof  of  the  indispensable  utility 
of  Logic,  and  the  consequent  refutation  of  the 
error  that  it  deals  only  with  the  forms  of 
thought  or  expression.  For  it  is  known  to  all 
logicians  that  the  most  serious  and  pernicious 
of  the  recognized  fallacies  are  those  that  relate 
to  the  matter  expressed  in  language,  and  are 
therefore  called  the  material  fallacies;  which 
by  logicians  generally  are  admitted  into  Logic, 
but,  as  it  were,  on  sufferance  only. 


PREFACE  vii 

(2)  The  second  fact  I  learned  was  that, 
though  it  is  impracticable  to  refute  such  errors 
otherwise  than  by  the  application  of  logical 
principles,  yet  owing  to  the  logical  decadence 
of  the  age,  and  the  general  disuse  of  Logic, 
this  mode  of  refutation  is  unavailable.  Hence 
under  existing  conditions,  there  is  no  practical 
means  of  stemming  the  tide  of  moral  and  politi- 
cal heresy  with  which,  with  increasing  violence, 
mankind  is  being  afflicted;  and  from  this  it 
follows,  as  a  necessary  inference,  that  the  first 
step  towards  reform  of  doctrine,  or  life,  in  any 
direction,  must  be  a  revival  of  the  study  and 
use  of  Logic.  My  work  therefore  is  the  result 
of  a  profound  realization  of  this  practical  neces- 
sity, and  of  the  imperative  demand  thus  result- 
ing. Nor — however  interesting  the  theory  of 
Logic  may  have  been  to  me — have  I  ever  lost 
sight  of  what  I  conceive  to  be  the  most  import- 
ant aspect  of  the  subject,  namely,  its  supreme 
practical  utility. 

Generally,  the  object  of  the  work  is  to  vindi- 
cate, as  against  modern  innovations,  the  old  or 
traditional  Logic.  This  constitutes  a  perfectly 
definite  body  of  doctrine,  rivalling  in  accuracy 
and  in  demonstrative  force  the  Geometry  of 
Euclid.  Nor  are  there  wanting  treatises  in 
which  its  theory  and  application  are,  on  the 
whole,  well  explained, — as,  e.  g.,  notably 
Whately's  work;  which,  notwithstanding  some 


Vlil  PREFACE 

manifest  defects,  still  remains,  not  only  the 
best,  but  the  only  elementary  exposition  of 
Logic,  in  the  English  language,  that  can  be 
recommended  to  the  student.  But  there  are 
many  reasons  why  a  mere  reproduction  of  the 
older  works  would  be  inadequate  for  our  present 
occasions,  to  some  of  which  I  will  briefly  ad- 
vert. 

The  first  of  these  relates  to  the  error,  already 
considered,  that  prevailed  with  many  of  the 
old  logicians,  as  with  the  new,  that  Logic  is 
concerned  only  with  the  forms,  and  not  with 
the  matter  of  thought,  or  its  expression.  For, 
though  this  defect  was  supplied  by  the  old 
logicians, — at  the  expense  of  their  consistency, 
— by  their  admirable  exposition  of  the  doctrines 
of  Definition  and  of  Classification  and  Division 
and  of  the  Term  generally,  and  of  the  Material 
or  so-called  Non-logical  Fallacies,  yet  their 
theory  of  Logic  remained  incomplete,  and 
Logic  was  thus  mutilated  of  some  of  its  most 
vital  parts. 

Again,  the  searching  investigation  to  which 
the  old  Logic  has  been  subjected  by  modern 
logicians,  though  its  general  effect  has  been  to 
vindicate  its  substantial  truth  and  to  re-estab- 
lish it  on  a  broader  and  firmer  basis,  has  yet 
resulted  in  several  additions  to  logical  doctrine, 
to  which  it  is  essential  that  the  attention  of  the 
student  should  be  directed.  Hence,  while  one 


PREFACE  ix 

of  the  principal  objects  of  this  work  is  to  vindi- 
cate the  truth  and  the  supreme  utility  of  Logic 
as  anciently  conceived,  it  is  also  contemplated 
to  supply  the  radical  defect  I  have  alluded  to, 
and,  at  the  same  time,  to  incorporate  with  the 
old  Logic  the  approved  results  of  modern  re- 
search ;  some  of  which  are  of  great  importance. 
It  remains  to  add  a  few  words  as  to  the 
method  and  style  with  which  the  subject  of 
the  work  is  treated.  Logic  is  admittedly  a 
demonstrative  or  apodictic  doctrine,  and  should 
therefore  be  treated  by  the  method  appropriate 
to  subjects  of  that  nature.  This  consists  in  the 
accurate  formulation  of  our  premises,  and  in 
reasoning  rigorously  from  them,  as  in  geome- 
try. But  this  method  demands  the  use  of 
a  style  altogether  different  from  that  in  com- 
mon use;  which  may  be  called  the  popular  or 
rhetorical.  For  it  is  the  peculiar  characteristic 
of  the  logical  style  that  it  must  be  accurate  or 
aphoristic,  i.  e.,  that  it  must  express  the  exact 
truth  without  any  admixture  of  error.  For 
the  same  truth  holds  good  in  ratiocination,  as 
in  nature  generally,  that  hybrids  are  unprolific; 
and  hence  the  slightest  admixture  of  error  in 
our  premises  will  render  them  altogether  use- 
less for  logical  inference.  Our  method  will 
therefore  demand  the  exact  analysis  of  the 
terms  we  use  and  the  formal  statement  of  our 
propositions;  which  to  the  general  reader  is 


X  PREFACE 

distasteful.  For  while  the  logical  style  ad- 
mits, and  even  requires,  great  brevity  of  ex- 
pression,—  so  that,  in  general,  volumes  of 
ordinary  disquisition  may,  by  means  of  it,  be 
compressed  into  a  brief  space, — yet  it  demands 
a  degree  of  attention  and  independent  thought 
that  only  a  few  highly  trained  or  exceptionally 
gifted  minds  are  willing  to  give,  or  perhaps 
without  great  exertion  are  capable  of  giving. 
But  this  is  nevertheless  essential  to  the  fruitful 
study  of  Logic,  as  of  apodictic  science  gener- 
ally. There  is  no  royal  road  to  Logic  any 
more  than  to  Geometry. 

The  best  type  of  this  style  is  found  in  the 
Mathematics,  and  especially  in  the  writings  of 
Euclid  and  the  geometers,  whose  style  and 
method  I  have  sought  to  emulate, — with  what 
success  remains  to  be  judged.  I  trust,  how- 
ever, I  may,  without  vanity,  say  of  the  result, 
with  Hobbes,  that  while  "  there  is  nothing  I 
distrust  more  than  my  elocution,  nevertheless 
I  am  confident,  excepting  the  mischances  of 
the  press,  it  is  not  obscure." 

GEORGE  H.  SMITH. 

Los  ANGELES,  February  26,  1900. 


CONTENTS 


INTRODUCTION  —  OF    THE    FUNCTION    OF 

LOGIC i 

BOOK  I 

THE  ANALYTIC  OF  RIGHT  REASONING 

CHAPTER  I 
RUDIMENTARY  NOTIONS        ....       23 


CHAPTER  II 
DOCTRINE  OF  THE  TERM 

I — OF  THE  NATURE  OF  THE  TERM 
II — OF  THE  SEVERAL  KINDS  OF  TERMS 
III — OF  THE  ANALYSIS  OF  TERMS 

CHAPTER  III 

DOCTRINE  OF  THE  PROPOSITION  . 

I — RUDIMENTS  OF  THE  DOCTRINE  . 
II— SEVERAL  THEORIES  OF  PREDICATION 
III — OF  THE  PREDICABLES 
IV — OF  THE  RELATIONS  BETWEEN  TERMS 


33 

33 

40 

44 


51 

55 
61 

64 


xi 


Xll  CONTENTS 

CHAPTER  IV 

PAGE 

DOCTRINE  OF  THE  SYLLOGISM       ...       74 

I — RUDIMENTS  OF  THE  DOCTRINE  ...        74 

II — THE  PRINCIPLE  OF  SUBSTITUTION         .          .        77 

III — OF  MATHEMATICAL  REASONING  ...       85 

CHAPTER  V 
SUMMARY  OF  THE  TRADITIONAL  LOGIC  .  91 

I — OF  THE  TRADITIONAL  LOGIC  GENERALLY     .        91 
II — THE  TRADITIONAL  DOCTRINE  OF  THE  PROP- 
OSITION      ......        92 

III — THE  TRADITIONAL  DOCTRINE  OF  THE   SYL- 
LOGISM       >  ...      104 

BOOK  II 
APPLIED  LOGIC 

PART  I 

OF  THE  METHOD  OF  LOGIC 

CHAPTER  VI 
OF  THE  LOGICAL  PROCESSES  .  .  .  123 

CHAPTER  VII 
THE  RULES  OF  LOGIC 137 

I — OF  THE  RULES  OF  LOGIC  GENERALLY          .      137 

II — RULES  OF  JUDGMENT         ....      142 

III — RULES  OF  INFERENCE         ....      145 


CONTENTS  Xlll 

PART  II 
DOCTRINE    OF   THE  FALLACIES 

CHAPTER  VIII 

PAGE 

DEFINITION    AND  CLASSIFICATION   OF   FAL- 
LACIES   .......     149 

CHAPTER  IX 

FALLACY  OF   NON-SIGNIFICANCE,   OR   NON- 
SENSE       157 

CHAPTER  X 
FALLACY  OF  FALSE  DEFINITION  .         .         .     168 

CHAPTER   XI 
ILLICIT    ASSUMPTION    OF   PREMISES   (Petitio 

Principii]         .         .         .         .         .  175 

CHAPTER  XII 
MISTAKING    THE    ISSUE    AND    IRRELEVANT 

CONCLUSION  (Ignoratio  Elenchi}      .         .188 

CHAPTER  XIII 
ILLICIT  CONVERSIONS    .....     198 

CHAPTER  XIV 

ILLICIT  SUBSTITUTIONS  OF  TERMS       .         .     200 
CHAPTER  XV 

EQUIVOCATION 203 

CHAPTER  XVI 

THE  TRADITIONAL  DOCTRINE  OF  FALLACIES.     210 

I — ARISTOTLE'S  CLASSIFICATION  OF  FALLACIES     .      210 

II — FALLACIES  in  Dictione  (EQUIVOCATION).          .      214 

III — OF  THE  FALLACIES  extra  Dictionem       .  .219 


LOGIC,  OR  THE  ANALYTIC  OF 
EXPLICIT  REASONING 


INTRODUCTION 

OF   THE    FUNCTION    OF    LOGIC 

§  i.  THE  THEORY  OF  KNOWLEDGE,  A  DE- 
PARTMENT OF  THE  THEORY  OF  OPINION. 
—The  problem  of  the  origin  and  nature  of 
knowledge  has  occupied  the  attention  of  the 
philosophers  for  something  over  twenty-five 
centuries  without  much  progress  toward  solu- 
tion. This  perhaps  results  from  the  fact  that 
the  problem  itself  is  but  part  of  a  larger  prob- 
lem" that  should  be  first  considered;  for  know- 
ledge is  but  a  species  of  opinion,  which  may  be 
either  true  or  false.  Hence  the  inquiry  as  to 
the  origin  and  nature  of  opinion  must  be  the 
first  in  order  of  investigation.  Nor  until  this 
investigation  has  been  made  will  we  be  pre- 
pared to  determine  the  specific  characteristics 


2  LOGIC 

by  which  true  knowledge  is  differentiated  from 
opinion  in  general. 

§  2.  KNOWLEDGE  BUT  VERIFIED  OPINION. 
— Men  generally  confound  this  distinction,  and 
regard  all  their  settled  opinions  or  beliefs  as 
knowledge.  This  is  not  merely  false,  but  ab- 
surd ;  for  not  only  do  the  opinions  of  men 
differ,  but  the  opinions  of  the  same  man  are 
often  inconsistent  and  contradictory  ;  and 
some,  it  is  clear,  must  be  false.  And  this  is 
apparent  also  from  the  nature  and  generation 
of  our  opinions.  For,  in  general,  these  come 
to  us  not  from  any  conscious  process,  but 
naturally  and  spontaneously  and  from  many 
sources,  as,  e.  g.,  from  testimony,  from  author- 
ity, from  inaccurate  observation  or  careless 
reasoning,  and  even  largely  from  mere  pre- 
judice or  bias.  Hence,  familiar  to  us  as  our 
opinions  are,  their  origin  in  general  is  as  un- 
known to  us  as  were  anciently  the  sources  of 
the  Nile;  nor  have  we  any  just  notion  of  the 
grounds  on  which  they  rest,  or  of  the  nature 
and  justice  of  their  demands  on  our  belief. 
Hence,  until  some  means  of  verifying  our 
opinions  be  found  and  applied,  we  can  have 
no  assurance  of  their  rectitude.  The  first  step 
in  Science  or  Philosophy  must,  therefore,  be 
to  distinguish  between  verified  and  unverified 
opinions.  The  former  constitutes  true  know- 
ledge or  science ;  the  latter — though  it  is  in 


INTRODUCTION'  3 

fact  the  stuff  out  of  which  most  of  the  current 
philosophy  is  woven  —  has  no  just  pretension 
to  the  name. 

§  3.  THE  SOURCES  OF  OPINION  DISTIN- 
GUISHED.— With  regard  to  the  source  of  our 
opinions,  we  must  distinguish  between  those 
derived  from  our  own  experience  and  those  de- 
rived from  the  experience  of  others;  of  which 
those  derived  from  the  common  experience  of 
mankind  are  the  most  extensive  and  important. 
The  last  have  come  to  us  by  means  of  lan- 
guage, which  may  therefore  be  said  to  be 
their  source;  nor  could  they  otherwise  have 
been  transmitted  to  us.  The  former  constitute 
— comparatively  speaking — but  a  small  and  in- 
significant part  of  the  sources  of  the  mass  of 
our  opinions.  For  the  greater  part  of  what 
we  know,  or  think  we  know,  is  not  original 
with  us,  but  has  come  to  us  from  others  by  or 
from  language.  The  distinction,  therefore,  is, 
not  between  opinions  derived  from  experience 
and  opinions  not  so  derived, —  for  it  may  be 
said  all  opinions  that  are  true,  or  rather  that  we 
know  to  be  true,  are  derived  ultimately  from 
experience,1 — but  in  the  manner  of  their  deri- 
vation ;  the  one  class  being  those  opinions  de- 
rived by  us,  each  from  his  own  experience,  the 
other,  those  derived  not  directly  from  our  own, 

1  The  distinction  made  in  the  text  is  of  fundamental  import- 
ance. The  necessity  of  a  constant  resort  to  experience  as  the 


4  LOGIC 

but  from  the  experience  of  others  from  or 
through  language. 

§  4,  OF  LANGUAGE  AS  A  RECORD  OF 
HUMAN  THOUGHT. — Of  the  two  classes  of 
opinions,  the  latter  is  infinitely  the  more  ex- 
tensive in  scope  and  important  in  character; 
for  all  that  men  have  seen  or  thought  or  felt 
has  been  expressed,  and  is  thus  preserved  to 
us  in  language;  which  thus  constitutes,  as  it 
were,  the  record  of  the  results  of  all  human 
experience  and  reason.  Here,  therefore,  is  to 
be  found  the  principal  source  of  our  opinions, 
verified  and  unverified  —  that  is  to  say,  not 
only  of  our  opinions  generally,  but  of  our 
knowledge  or  science.  But,  regarding  lan- 
guage as  a  record  and  source  of  opinion,  we 
must  distinguish  between  the  forms  in  which 
opinion  is  embodied  in  it.  These  forms  may 
be  described,  with  sufficient  accuracy  for  our 
purposes,  as  consisting  in  terms,  propositions, 
and  syllogisms.  But  of  these  the  syllogism  in 
its  end  and  effect  is  but  the  reduction  of  two 

ultimate  source  of  our  knowledge  cannot  be  too  strongly  in- 
sisted upon.  But  to  construe  this  proposition  as  referring  to 
each  man's  individual  experience  is  to  fall  into  an  error  of  the 
kind  called  by  Bacon  "  Idols  of  the  Den"  ;  and  thus  to  fall 
under  the  reproach  of  Heraclitus  "  that  men  search  for  know- 
ledge in  lesser  worlds,  and  not  in  the  greater  or  common 
world,"  i.  e.,  the  great  world  of  the  common  notions  of  man- 
kind, derived  from  the  universal  experience  and  embodied  in 
the  common  language.  (Nov,  Org.,  bk.  i.,  aph.  xliii.) 


IN  TROD  UC  TION  5 

propositions  to  one,  and,  in  this  connection,  is 
of  interest  to  us  merely  as  exhibiting  one  of 
the  modes  in  which  opinion  is.formed.  It  will 
be  sufficient,  therefore,  to  distinguish  the  term 
and  the  proposition  as  the  two  forms  in  which 
opinions,  or  the  elements  of  opinions,  are  em- 
bodied. But  the  proposition  is  itself  of  two 
kinds,  differing  essentially  in  nature.  In  the 
one — if  not  an  inference — it  is  simply  the  state- 
ment of  a  relation  intuitively  perceived  to  exist 
between  two  terms  or  names,  that  is  to  say, 
between  the  notions  or  concepts  denoted  by 
them, — as,  e.  g.,  where  we  say,  "  Bodies  are 
affected  by  gravity,"  or  "  Two  islands  cannot 
be  contiguous,"  or  "  Fishes  live  in  the  sea," 
or  "  Man  is  rational";  in  the  other,  it  is  a 
statement  of  a  relation  between  terms,  not  in- 
tuitively perceived — or  logically  inferred — but 
assumed  to  be  true  from  testimony  or  other- 
wise,— as,  e.  g.,  where  we  say,  ''  Brutus  was 
one  of  the  murderers  of  Caesar,"  or  "  Hannibal 
was  conquered  by  the  Romans."  The  former 
-  in  accordance  with  the  definitions  used 
throughout  this  work — will  be  called  a  judg- 
ment ;  the  latter,  an  assumption.  In  the  former 
case  the  truth  of  the  proposition  is  involved  in 
the  meanings  of  the  terms, — i.  e.,  in  the  nature 
of  the  concepts  or  notions  denoted  by  them ; 
and  this  is  true  also  of  all  inferences,  or  propo- 
sitions inferred  from  judgments.  So  that  with 


6  LOGIC 

relation  to  all  such  propositions,  whether  in- 
tuitively perceived  or  inferred,  the  original 
sources  of  opinion  are  the  notions  or  concepts 
in  which  they  are  involved.  We  may  therefore 
distinguish,  as  the  two  sources  of  opinion  af- 
forded us  by  language,  (i)  the  notions  or  con- 
cepts expressed  in  terms,  and  (2)  assumptions, 
or  assumed  propositions. 

With  the  truth  of  the  latter,  or  the  evidence 
on  which  they  rest  for  credence,  Logic  is  not 
concerned;  nor  is  it  concerned  with  them  in 
any  way,  except  as  premises  from  which  to 
argue ;  or  to  reject  them  as  such,  if  they  can  be 
shown  by  logical  processes  to  be  false.  But 
where  such  propositions  are  justified  by  experi- 
ence, and  come  thus  to  be  generally  received, 
the  result  universally,  or  almost  universally,  is 
the  generation  of  a  new  notion, — i.  e.,  the 
notion  of  the  relation  perceived  between  its 
terms;  which  is  either  expressed  in  a  new  term 
or  added  to  the  content  or  meaning  of  an  exist- 
ing term;  and  this,  indeed,  to  the  extent  it  is 
attainable,  is  the  end  of  science,  and,  in  a  per- 
fect language, —  were  such  attainable, —  would 
be  the  general  result.  Thus  the  general  pro- 
gress of  human  thought  consists  largely  in  the 
conversion  of  propositions  into  terms  or  names 
denoting  the  relations  expressed  in  them  ;  and 
hence,  generally,  in  terms  are  contained  many 
propositions,  as,  e.  g.,  in  "  gravity,"  '  justice," 


INTRODUCTION  / 

etc. — in  the  former  of  which  is  contained  a  large 
part  of  Physical  Science,  and  in  the  latter  nearly 
the  whole  theory  of  the  State.  In  this  way  the 
stock  of  the  common  notions  of  mankind  is 
continuously  accumulated,  until  it  may  be  said 
that  the  great  part  of  all  that  has  been  achieved 
in  thought  by  men  is  expressed  or  implied  in 
terms  or  names.  Here,'  therefore,  are  to  be 
found  the  principal  sources  of  opinion ;  and, 
compared  with  these,  opinions  embodied  in 
propositions  that  cannot  be,  or  have  not  been, 
reduced  to  single  notions  are  limited  in  ex- 
tent, and  of  secondary  importance.  And  this 
is  especially  true  with  regard  to  the  Moral 
Sciences;  under  which  name  I  include  all  the 
various  branches  of  the  science  of  human 
nature;  for  in  these  sciences  it  is  impossible 
to  conceive  of  any  rudimentary  notion  or 
thought  that  has  not,  in  the  long  history  of 
man,  been  conceived  by  the  human  mind  and 
embodied  in  terms.  With  reference,  therefore, 
to  all  that  has  been  achieved  in  science  or  in 
popular  thought,  the  sources  of  all  our  opin- 
ions, verified  and  unverified, — that  is  to  say, 
of  all  our  knowledge  or  supposed  knowledge, 
—  are  to  be  sought  in  language,  and,  prin- 
cipally, in  the  notions  expressed  in  terms  or 
or  names ' ;  and  consequently,  with  reference  to 

1  If  the  reader  will  thoroughly  apprehend  this  proposition, 
he  will  find  in  it  the  key,  not  only  to  Logic,  but  to  all  Phil- 


8  LOGIC 

knowledge  or  supposed  knowledge  of  this  kind, 
our  method  must  consist  in  the  study  of  lan- 
guage. 

§  5.  RECEIVED  OPINION  DISTINGUISHED 
FROMTRUE  KNOWLEDGE. — Our  opinions,  how- 
ever, are  derived  from  this  source  in  two  ways, 
which  must  be  distinguished  :  namely,  by  tradi- 
tion,— by  which  our  opinions  are  delivered  to 
us  ready  made  in  the  form  of  propositions,— 
and  by  reasoning  upon  the  notions  embodied 
in  terms.  For  the  thought  contained  in  lan- 
guage is  embodied  in  two  ways,  namely, 
explicitly,  in  the  form  of  propositions,  and 
implicitly,  in  terms;,  and  of  propositions, —  as 
we  have  seen, — many  are  but  explicit  state- 
ments of  what  is  implied  in  the  notions 

osophy.  The  elements  of  knowledge,  so  far  as  already 
achieved,  we  repeat,  are  the  notions  or  concepts  incarnate  in 
terms ;  and  these  must  always  constitute  the  principal  source 
of  our  knowledge  ;  for,  in  comparison  with  the  knowledge 
thus  expressed  or  implied,  the  original  contributions  of  the 
most  gifted  of  men  to  the  common  stock  must  be  inconsider- 
able. Nor  can  any  such  contribution  to  the  knowledge  of 
mankind  be  regarded  as  completely  achieved  until  embodied 
in  definite  terms ;  and  hence  the  formation  of  such  terms,  or, 
what  is  the  same,  of  the  notions  embodied  in  them,  must  be 
regarded  as  the  end  of  scientific  discovery.  There  is,  there- 
fore, nothing  paradoxical  in  the  assertion  of  Condillac  that 
"  Science  is  but  language  well  made."  Hence,  to  repeat  what 
has  been  said,  it  is  to  the  common  stock  of  notions  thus  gradu- 
ally accumulated  by  mankind  and  permanently  secured  by  ex- 
pression in  terms,  that  we  must  resort  as  the  principal  source 
of  all  knowledge  or  science.  See  Appendix  A. 


INTRODUCTION  9 

expressed  in  terms,  as,  e.  g.,  in  the  prop- 
osition, "  All  bodies  are  affected  by  grav- 
ity," etc.  With  reference  to  these,  though 
they  may  be  true,  their  mere  reception  cannot 
be  said  to  constitute  knowledge;  but  —  in  the 
proper  sense  of  the  terms — we  can  know  them 
only  when  we  have  reasoned  them  out  for  our- 
selves from  the  primary  notions  in  which  they 
are  involved;  as,  e.  g.,  in  the  Mathematics, 
where  we  cannot  be  said  to  have  mastered  a 
theorem  until  we  are  able  to  work  it  out  from 
the  premises  by  the  exertion  of  our  own  powers 
unassisted  by  memory.  With  reference  to  all 
that  has  been  achieved  in  thought,  therefore, 
our  method  in  the  pursuit  of  knowledge  must 
begin  with  the  apprehension  of  the  notions 
already  formed  by  men  and  embodied  in  terms; 
and  this  involves  the  testing  of  those  notions 
for  ourselves  by  comparing  them  with  the 
realities  to  which  they  are  supposed  to  corre- 
spond. 

$  6.  THE  PHYSICAL  AND  MATHEMATICAL, 
DISTINGUISHED  FROM  THE  MORAL  SCIENCES. 
-These  observations  apply  equally  to  the 
Physical  and  Mathematical  as  to  the  Moral  Sci- 
ences ;  but  there  are  differences,  partly  essential 
and  partly  accidental,  between  the  two  classes 
of  sciences,  which  must  be  adverted  to  ' : 

(i)    In    the    Physical    Sciences    and    in    the 

1  See  Appendix  B. 


IO  LOGIC 

Mathematics,  technical  terms  expressing  ac- 
curately the  concepts  or  notions  involved  are 
exclusively  used,  but  in  the  Moral  Sciences  it 
is  otherwise;  for  there  the  notions  developed 
by  the  experience  and  reasoning  of  mankind— 
which  must  always  constitute  the  principal 
source  of  our  knowledge — are  in  general  loosely 
and  inaccurately  expressed,  and  the  same  vocal 
sign,  or  vocable,  is  commonly  used  to  denote 
many  different  notions  more  or  less  nearly  re- 
lated ;  nor,  with  reference  to  these,  does  the 
term  in  general  express  the  notion  accurately. 
Hence  the  necessity  of  definition,  which  is  at 
once  the  fundamental  and  the  most  difficult 
of  the  logical  processes.  But  in  the  Physical 
Sciences  the  notion  is  always  accurately  defined 
by  the  thing  itself;  and  so  in  the  Mathematics, 
though  highly  abstract,  our  notions  are  always 
clearly  defined.  Thus  in  these  sciences  the 
logical  processes  are  so  simple  that  it  is  impos- 
sible to  err,  unless  by  inadvertence,  and  all 
errors  are  quickly  corrected  ;  and  hence  a  tech- 
nical knowledge  of  Logic  is  but  little  needed.' 
But  in  the  Moral  Sciences  it  is  different,  for 
here  the  difficulty  of  defining  our  terms  is 

1  Hence,  from  disuse  of  the  more  difficult  of  the  logical 
processes,  a  man  in  the  former  case,  may  be  a  competent 
naturalist  without  being  much  of  a  reasoning  creature  ;  and 
in  the  latter,  a  great  mathematician  and  yet  a  child  in  the 
practical  affairs  of  life,  individual  and  social. 


IN  TROD  UC  TION  1 1 

great,  and  often  insuperable,  and  hence,  in  the 
prosecution  of  these  sciences,  Logic  must 
always  be  an  indispensable  instrument. 

(2)  To  a  certain  extent  this  difference   be- 
tween the  two  classes  of  sciences  is  an  essential 
one,  and  cannot  be  altogether  removed.     But 
to  a  large  degree  the  Moral  Sciences  are  sus- 
ceptible of  apodictic  treatment,  and  by  such 
treatment    may  be  indefinitely  assimilated  in 
nature  to  what  are  commonly  called  — though 
not    exclusively    entitled    to    the    name  —  the 
Exact  Sciences;  for  a  large  part  of  the  Moral 
Sciences,  including  nearly  all  the  fundamental 
principles   upon   which   they   rest,    are  purely 
apodictic.     For,  though  it  is  commonly  sup- 
posed there  is  an  essential  difference  between 
Mathematical  and  what  is  called  Moral  Reason- 
ing, this  is  not  true;  all  ratiocination  (not  fal- 
lacious) is  essentially  of  the  same  character  and 
equally  conclusive.1 

(3)  Hence  it  may  be  observed  as  a  corollary, 

1  This  is  much  insisted  upon  by  Locke  :  "  Confident  I 
am,"  he  says,  "that  if  men  would,  in  the  same  method,  and 
with  the  same  indifferency,  search  after  moral,  as  they  do  after 
mathematical  truths,  they  would  find  them  to  have  a  stronger 
connection,  one  with  another,  and  a  more  necessary  conse- 
quence from  our  clear  and  distinct  ideas,  and  to  come  nearer 
a  perfect  demonstration  than  is  commonly  supposed  "  (Essay, 
bk.  iv.,  chap,  iii.,  20).  "By  what  steps  we  are  to  proceed 
.  .  .  is  to  be  learned  in  the  school  of  the  mathematicians, 
who,  from  very  plain  and  easy  beginnings,  by  gentle  degrees, 


12  LOGIC 

the  principal  task  before  us,  with  reference  to 
the  Moral  Sciences,  is  to  reduce  them  as  far  as 
possible  to  apodictic  or  scientific  form.  This, 
under  present  conditions,  will  still  leave  an  im- 
mense field  of  investigation  in  which  we  must 
resort  directly  to  experience,  and  especially  to 
experience  as  embodied  in  history  and  statis- 
tics; but  until  all  that  is  susceptible  of  being 
so  reduced  is  reduced  to  scientific  form,  no 
progress  can  be  made  in  dealing  with  matters 
depending  upon  experience. 

(4)  With  regard  to  the  Physical  Sciences 
another  difference  is  to  be  noted,  namely, 
between  what  has  been  achieved  and  the  dis- 
covery of  new  facts;  with  reference  to  which 
the  instrument  of  discovery  is  mainly  experi- 
ment and  observation,  or,  as  it  is  commonly 
called,  the  Inductive  Method.  In  this  respect 
these  differ  from  the  Moral  Sciences,  where, 
though  the  same  method  must  always  be  used, 
its  function  is  confined  chiefly  to  the  process  of 
definition.1 

and  a  continued  chain  of  reasonings,  proceed  to  the  discovery 
and  demonstration  of  truths  that  appear  at  first  sight  beyond 
human  capacity  "  {Id.,  bk.  iv.,  chap,  xii.,  7,  8).  "  This  gave 
me  confidence  to  advance  the  conjecture  which  I  suggest, 
Chap,  iii.,  viz.,  that  Morality  is  capable  of  demonstration  as 
well  as  Mathematics." 

1  The  nature  of  Logic,  and  of  the  relation  of  the  Inductive 
Method  to  Logic,  is  thus  precisely  expressed  by  Bacon  : 

"  The   syllogism   consists   of   propositions,   propositions  of 


INTRODUC  TION  1 3 

§  7.  OF  THE  MODES  IN  WHICH  OPINION 
is  GENERATED. —  With  reference  to  results 
achieved  and  embodied  in  language,  and  to 
our  opinions  generally,  the  process  by  which 
our  notions  or  concepts  are  derived  is  the  re- 
verse of  what  is  commonly  supposed.  In  the 
discovery  of  new  facts,  or  the  formation  of  new 
concepts,  we  commence  with  the  conception  of 
the  concrete,  and,  the  concept  being  formed, 
we  find  the  name.  But  this,  in  the  develop- 
ment of  thought  at  which  we  have  arrived,  can 
occur  only  in  the  Physical  Sciences.  For,  as 
we  have  observed,  it  is  hardly  probable  that 
in  the  Moral  Sciences  any  rudimentary  thought 
can  ever  occur  that  has  not  already  occurred 
to  some  one  and  been  expressed  in  language. 
Hence,  with  regard  to  all  matters  dealt  with 
in  the  Moral  Sciences  (as  also  in  the  Physi- 
cal Sciences  with  regard  to  results  already 
achieved),  the  order  of  our  cognitions  is,  first, 
to  learn  the  words,  — /.  e.,  the  word-signs  or 

words,  words  are  the  signs  of  notions.  If,  therefore,  the 
notions  (which  form  the  basis  of  the  whole)  be  confused  and 
carelessly  abstracted  from  things,  there  is  no  solidity  in  the 
superstructure.  Our  only  hope  then  is  in  genuine  induction  " 
(Nov.  Org.,  bk.  i.,  aph.  xiv). 

The  subject  is  more  fully  developed  in  aph.  lix.,  and  beauti- 
fully illustrated  in  aph.  xcv.  See  also  his  doctrine  of  Idols, 
aph.  xxxviii.  et  seq.  It  may  be  observed  here,  in  passing,  that 
no  student  of  Philosophy,  and  still  less  of  Logic,  can  afford  to 
neglect  the  first  book  of  the  Novum  Organum  or  the  De 
A  ugmentis. 


14  LOGIC 

vocables, — and    afterwards,   the    concepts   or 
notions  expressed  in  them.' 

§  8.  OUR  SUPPOSED  KNOWLEDGE  OFTEN 
NONSENSE. — And  as  the  latter  function — out- 
side the  Exact  Sciences  —  is  in  general  very 
lamely  performed,  the  result  is  that  the  greater 
portion  of  our  supposed  knowledge  in  abstract 
matters  consists  of  words  without  definite 
notions  attached  to  them,  and  is  therefore 
merely  nonsense.  For  when  we  reason  with 
undefined  or  ill-defined  terms  we  are  dealing 
with  mere  delusions  or  dreams  —  like  Ixion 
embracing  clouds  and  begetting  monsters. 
Thus,  e.  g. ,  when  we  assert,  with  Bentham  and 
Austin,  that  General  Utility  is  the  ultimate 
test  or  principle  by  which  the  just  and  the  un- 
just and  right  and  wrong  generally  are  to  be 
determined,  we  are  in  fact  talking  nonsense; 
for  it  cannot  be  determined  from  this  expres- 
sion whether  we  have  in  view  the  welfare  of  a 
mere  majority,  or  two  thirds,  or  three  fourths, 
or  other  proportion  of  mankind,  and  hence 
from  this  premise  all  sorts  of  extravagant 
opinions  are  deduced.  Hence  the  mass  of  us 

1  The  logicians,  from  and  including  Hamilton,  have  en- 
tirely overlooked  this  distinction,  and  have  thus  substituted 
for  the  old  logical  doctrine  of  Simple  Apprehension,  the  psy- 
chological doctrine  of  Conception, — a  doctrine  necessary  to  be 
understood,  but  which  is  concerned  rather  with  the  original 
formation  of  language  than  with  its  use  as  an  instrument  of 
reasoning. 


INTRODUCTION  15 

generally,  and  all  of  us  in  many  matters, — like 
Moliere's  hero,  who  was  surprised  to  find  that 
he  had  been  talking  prose  all  his  life, — have  all 
our  lives  been  talking  nonsense.1  And  this  is 
true  not  only  of  opinions  commonly  regarded 
as  nonsensical,  but  of  all  opinions  involving 
either  undefined  notions  or  notions  to  which 
there  are  no  corresponding  realities. 

§  9.  THE  CRITICAL  SPIRIT  ESSENTIAL  TO 
WISDOM.  —  Our  wisdom  is  therefore  to  be 
measured,  not  by  the  extent  of  our  learning, 
or  by  knowledge  of  detached  facts,  or  by  vivac- 
ity of  thought  or  expression,  or  by  the  confi- 
dence of  our  belief,  but  chiefly  by  the  capacity 
to  judge  our  supposed  knowledge,  and  to  de- 
tect its  falsity  or  non-significance.  In  this  way 
Socrates  modestly  explained  the  oracle  of  the 
Delphic  god,  that  he  was  "  the  wisest  of  man- 
kind." For,  he  said,  he  alone  had  discovered 
that  all  men  were  ignorant,  including  himself; 
but  others  mistook  their  ignorance  for  know- 
ledge.2 We  conclude,  therefore,  as  we  began, 
that  what  we  regard  as  our  knowledge  consists 
mainly  of  unverified  opinions  or  beliefs,  and 
that  however  firmly  these  may  be  established, 

1  See  Appendix  C. 

2  As  explained  by  Grote  (cited  infra,  §  16,  App.  H),  the  thesis 
of  Socrates  was  that  "  the  natural  state  of  the  human  mind  " 
is  "not  simply  ignorance,  but  ignorance  mistaking  itself  for 
knowledge." 


l6  LOGIC 

or  however  passionately  they  may  be  asserted 
and  believed,  they  do  not  necessarily,  or  even 
generally,  constitute  true  knowledge.  Hence, 
until  we  are  enabled  to  distinguish  the  true 
from  the  false,  we  can  have  no  assurance  of 
their  rectitude  or  truth. 

§  10.  LOGIC  THE  ULTIMATE  TEST  OR  CRI- 
TERION OF  TRUTH.  —  We  must,  therefore, 
seek  some  tests  or  criterions  —  if  any  there  be 
—  by  which  the  truth  or  falsity  of  our  beliefs 
may  be  determined ;  and  of  such  two  only  can 
be  conceived  ;  namely,  Experience  and  Reason- 
ing, or  Logic.  Of  these  the  former  is  more  or 
less  efficiently  used  by  men  in  general ;  and  in 
concrete  matters  and  in  the  ordinary  familiar 
affairs  of  life,  its  operation  is  moderately  satis- 
factory. For  thus,  by  actual  contact  with  the 
hard  facts  of  our  experience,  our  opinions  or 
beliefs  are,  to  a  large  extent  effectually,  and 
often  painfully,  modified  and  corrected.  But 
the  function  of  experience  is  simply  to  furnish 
Reason  with  materials  on  which  to  work;  and 
of  Reasoning,  or  Logic,  as  Hobbes  says:  "  So 
far  are  the  mass  of  men  from  using  it,  that 
they  do  not  even  know  what  it  is." 

1  "  The  most  part  of  men,  though  they  have  the  use  of  rea- 
soning a  little  way,  as  in  numbering  to  some  degree,  yet  it 
serves  them  to  little  use  in  common  life  ;  in  which  they  gov- 
ern themselves,  some  better,  some  worse,  according  to  their 
differences  of  experience,  quickness  of  memory,  and  inclina- 
tion to  several  ends ;  but  especially  according  to  good  or  evil 


IN  TROD  UC  TION  1 7 

§  ii.  THE   DECADENCE  OF  THE  AGE  IN 

LOGIC  AND  THE  MORAL  SCIENCES. — And  this 
is  true  not  only  of  the  common  people,  but  of 
the  educated,  and  even  of  the  philosophers  and 
the  professors;  who  in  the  last  century,  owing 
to  the  disuse  of  Logic,  have  in  fact  lost  the 
very  idea  of  it;  so  that  in  our  schools  and 
universities,  under  the  name  of  Logic,  any- 
thing but  Logic  itself  is  taught,  and  it  has  thus 
become  a  lost  art.1  Yet,  obviously,  in  all 
abstract  matters,  and  especially  in  Morality, 
Politics,  and  all  the  different  branches  of  the 
Science  of  Human  Nature,  experience,  while 
useful  to  us,  can  go  but  a  little  way,  and 
therefore  Logic  must  be  an  indispensable  in- 
strument. Hence  it  is  to  the  disuse  of  Logic 
that  the  existing  incoherent  and  chaotic  state 
of  the  Moral  Sciences  is  to  be  attributed."  It 
may  therefore  be  confidently  hoped  that  by  the 
renewed  use  of  Logic  a  revival  of  these  sciences 
is  to  be  anticipated,  vying  in  extent  with  that 
of  the  concrete  sciences  in  modern  times,  and 

fortune,  and  the  errors  of  one  another.  For  as  for  'science,' 
or  certain  rules  of  their  actions,  they  are  so  far  from  it  that 
they  know  not  what  it  is"  (Lev.,  chap.  v.). 

1  "  We  live  in  an  age,"  says  De  Morgan,  "  in  which  formal 
logic  has  long  been  banished  from  education  ;  entirely  we 
may  say  from  the  education  of  the  habits."  The  proposition 
is  even  truer  of  the  present  day  ;  for  in  De  Morgan's  time 
there  still  survived  some  of  the  old  style  of  logicians. 

*  See  Appendix  D. 


1 8  LOGIC 

far  surpassing  them  in  practical  utility  to  the 
human  race.1 

§  12.  OF  AUTHORITY  AND  PREJUDICE. — I 
would  not,  however,  in  thus  explaining  and 
commenting  upon  the  general  dominance  of 
authority  and  prejudice  over  men,  be  under- 
stood as  altogether  condemning  it.  Under 
existing  conditions,  and  perhaps  under  all  con- 
ditions, the  opinions  of  the  masses  of  mankind, 
in  Politics  and  other  matters  of  common  con- 
cern, must  be  determined  mainly  by  custom  and 
authority.  Hence  the  distinction  made  by  the 
old  philosophers  between  their  esoteric  and  ex- 
oteric doctrines;  the  latter  consisting  of  those 
that  could  be  taught  to  the  masses,  the  former, 
of  those  that  required  the  peculiar  training  of 
the  philosopher  to  comprehend  —  a  profound 
distinction  that  has  been  lost  in  modern  times. 
But  though  it  may  not  be  possible,  or  perhaps 
even  desirable,  to  make  all  men  philosophers, 
yet  it  is  possible  to  make  the  masses  of  them 
logical  in  the  matters  with  which  they  are  con- 

1  The  argument  of  Demosthenes  in  the  first  Philippic  may 
be  readily  applied  to  the  proposition  asserted  in  the  text : 
"  First  I  say,  you  must  not  despond,  Athenians,  under  your 
present  circumstances,  wretched  as  they  are  ;  for  that  which  is 
worst  in  them  as  regards  the  past  is  best  for  the  future. 
What  do  I  mean?  That  your  affairs  are  amiss,  men  of 
Athens,  because  you  do  nothing  that  is  needful ;  if,  not- 
withstanding you  performed  your  duties,  it  were  the  same, 
there  would  be  no  hope  of  amendment." 


INTRODUCTION  19 

versant ' ;  and  for  those  who  aspire  to  be  lead- 
ers of  opinion,  Logic  is  essential.  For  these, 
if  worthy  of  the  function  to  which  they  aspire, 
cannot  afford  to  be  deficient  in  this  respect; 
they  must  either  be  logicians,  or  false  prophets, 
or  blind  leaders  of  the  blind. 

§  13.  PLAN  OF  THE  WORK.— Though  I  re- 
gard the  study  of  Logic  as  essential  to  the  cul- 
tivation and  the  use  of  the  reasoning  powers, 
— and  hence  as  indispensable  to  the  Moral  Sci- 
ences,— yet  it  is  chiefly  as  a  test  or  criterion  of 
fallacy  that  I  propose  to  treat  it.  This  use  of  it 
will,  of  course,  necessitate  some  consideration 
of  the  elementary  principles  and  rules  of  Logic 
as  necessary  to  the  understanding  of  the  Doc- 
trine of  the  Fallacies.  But  this  part  of  my  essay 
will  be  abbreviated  to  the  utmost  extent  con- 
sistent with  this  object ;  that  is  to  say,  I  will 
try  to  include  everything  essential  to  the  under- 
standing of  the  rudiments  of  Logic,  but  noth- 
ing more.  If  I  should  fail  in  this,  and  anything 
necessary  should  be  omitted,  the  defect  may 
be  readily  obviated  by  reference  to  the  work 
of  Whately,  who,  among  elementary  writers, 
may  be  regarded  (in  any  true  sense  of  the 
word)  as  the  last  of  the  logicians. 

The  subject  will  be  treated  in  two  books,  the 
first  entitled  "  The  Analytic  of  Right  Reason- 
ing," the  second,  "  Applied  Logic  "  ;  the  latter 

1  See  Appendix  E. 


2O  LOGIC 

of  which  will  include  two  subjects,  namely: 
'  The  Method  of  Logic  "  and  "  The  Doctrine 
of  the  Fallacies,"  or  "  The  Analytic  of  Wrong 
Reasoning."  In  treating  of  the  last,  the  ex- 
amples of  the  several  fallacies  will  be  taken 
almost  exclusively  from  current  theories  of 
Politics  and  Morality.  Our  examples  will 
therefore  consist,  not  of  mere  trivialities, 
such  as  are  so  common  in  books  on  Logic, 
but  of  fallacies  that,  in  perverting  moral  and 
political  theory  and  in  corrupting  practice, 
have  dominated,  and  still  continue  to  domi- 
nate, the  fortunes  of  mankind.  They  come 
to  us,  therefore,  as  veterans  of  what  Hobbes 
calls  the  "  Kingdom  of  Darkness,"  crowned 
with  the  laurels  of  victory.1 

1  Lev.,  chap.  xliv. :  see  Appendix  F. 


BOOK  I 

THE  ANALYTIC  OF  RIGHT 
REASONING 


21 


BOOK  I 

THE  ANALYTIC  OF  RIGHT 
REASONING 


CHAPTER  I 

RUDIMENTARY  NOTIONS 

§  14.  DEFINITION  OF  LOGIC  AND  OF  IN- 
VOLVED TERMS.— Logic  is  defined  by  Whately 
as  the  science  and  also  the  art  of  reasoning. 
Reasoning  may  be  defined  as  consisting  in  the 
exercise  of  the  comparative  or  discursive  fac- 
ulty of  the  mind — that  is  to  say,  the  faculty  by 
which  our  notions  or  concepts  are  compared 
with  each  other,  and  with  the  realities  to  which 
they  are  supposed  to  correspond,  and  their  re- 
lations with  each  other,  and  with  such  realities 
are  perceived.  Or  we  may  define  reason  as 
the  faculty,  and  reasoning  as  consisting  in  its 
exercise.1  But  Logic — by  which  I  mean  the 

1  The  terms  reason  and  reasoning,  though  conjugate,  have 
unfortunately  been  divorced  by  logicians,  and,  following 

23 


24  LOGIC 

traditional  Logic  —  is  not  to  be  regarded  as 
having  to  deal  with  reasoning  in  general,  but 
with  explicit  reasoning  only,  or  ratiocination ; 
which  may  be  defined  as  reasoning  expressed 
in  language,  or,  so  far  expressed  that  the  miss- 
ing parts  are  understood.  Hence  it  is  rightly 
said  by  Whately  that  Logic  is  exclusively  con- 
versant with  language;  by  which  is  meant,  not 
merely  the  signs  of  thought,  but  also  the 
thought  signified.1  This  follows  from  the 
definition,  and  also  from  considering  the  sev- 
eral subjects  of  which  it  treats,  which,  by  the 
universal  consensus  of  logicians,  consist  of  the 
Doctrines  of  the  Term,  of  the  Proposition,  and 
of  the  Syllogism.  But  all  these  are  simply 
parts  or  kinds  of  language. 

§  15.  RATIOCINATION  DEFINED. — But  Ra- 
tiocination, being  a  species  of  reasoning,  must 
consist  in  the  comparison  of  concepts  or 
notions,  and  these,  in  order  to  fall  within  the 
province  of  Logic,  must,  ex  vi  termini,  be  ex- 
pressed in  terms.  Hence,  Ratiocination  must 
be  defined  as  consisting  in  the  process  of  com- 

them,  by  lexicographers  generally  ;  and  accordingly  Locke 
is  blamed  by  Whately  for  confounding  them.  But  in  this 
Locke  is  right,  and  the  logicians  wrong  ;  and  the  usage  of  the 
latter  has  been  the  source  of  infinite  confusion  in  Logic.  As  I 
use  the  terms,  Reason  includes  the  faculties  of  Inference, 
Judgment,  and  Simple  Apprehension  ;  and  Reasoning  the 
corresponding  processes. 
1  See  Appendix  G. 


RUDIMENTARY  NOTIONS  2$ 

paring  terms,  with  the  view  of  perceiving  their 
relations.  And  this  necessarily  implies,  also, 
the  process  of  determining  the  meaning  of  the 
terms  compared,  or,  in  other  words,  the  process 
of  definition. 

§  16.  LOGIC  DEFINED. — Logic,  regarded  as 
a  theory,  may,  therefore,  be  defined  as  the 
Analytic  of  Explicit  Reasoning,  or  of  Ratio- 
cination—  meaning,  by  this  expression,  the 
systematized  results  of  an  analysis  of  the  pro- 
cesses involved  in  ratiocination.1  And  its 
practical  end  is  to  determine  the  meanings  of 
terms  and  the  relations  between  the  concepts 
or  notions  denoted  by  them.3 

§  17.  OF  THE  SEVERAL  KINDS  OF  TERMINAL 
RELATIONS. — The  relations  between  terms  are 
of  two  kinds,  which  may  be  called  immediate 
and  inferred ;  and  the  former,  again,  are  of 
two  kinds,  that,  for  lack  of  better  names,  may 
be  called  intuitive  and  quasi-intuitive. 

§  18.  THE  INTUITIVE  RELATIONS  OF  TERMS. 
— Of  the  former  kind  are  all  those  relations 
between  terms  that  are  intuitively  perceived 
upon  comparing  them  together,  as,  e.  g.,  the 

1  See  Appendix  H. 

2  "  Knowledge  [is]  but  the  perception  of  the  connection  and 
agreement  or  disagreement  or  repugnancy  of  any  of  our  ideas  " 
(Locke,  cited  §110  n.  g.  App.  N).     "  Knowledge  is  not  so 
much  increased  by  a  continued  accession  of  new  ideas  as  by 
perceiving  the  relations  of  those  ideas  which  we  have  already 
acquired  "  (Eunomos,  cited  Chitty's  Blackstone,  introd.  note). 


26  LOGIC 

relation  of  species  and  genus  between  the  class 
of  beings  denoted  by  the  term  man  and  the 
class  denoted  by  the  term  rational,  or  between 
the  classes  denoted  by  the  terms  horse  and 
animal,  or  the  relation  of  mutual  exclusion 
existing  between  the  terms  of  the  proposition, 
No  two  islands  can  be  contiguous." 
§  19.  JUDGMENT  DEFINED. — The  perception 
of  a  relation  of  signification  between  two  terms 
is  called  Judgment;  which  may  be  defined  as 
the  intuitive  perception  of  a  significative  rela- 
tion between  two  terms.  The  result  of  the 
process  is  called  a  judgment;  which  may  be 
defined  simply,  as  a  self-evident  proposition. 

§  20.  THE  QUASI-INTUITIVE  RELATIONS 
OF  TERMS. — Analogous  to  the  intuitive  rela- 
tions of  terms  are  the  relations  between  the 
terms  of  all  assumed  propositions,  or  assump- 
tions; for  these,  though  not  intuitively  true, 
are  assumed  or  supposed  to  be  such  for  the 
sake  of  the  argument,  and  used  as  principles 
from  which  to  reason ;  they  may,  therefore,  be 
regarded  as  quasi-intuitive^  Under  this  head 

1  We  borrow  this  form  of  expression  from  the  lawyers,  who 
find  it  indispensable,  as,  e.  g.,  in  the  expressions  quasi-torts, 
quasi-contracts"  etc.  As  we  are  informed  by  Cicero,  the 
Epicureans  held  that  the  gods  had  not  bodies,  but  quasi- 
bodies  only,  i.  e.,  something  like  bodies.  An  Indian  com- 
munity, I  have  read  somewhere,  were  much  annoyed  by  a 
species  of  animal  something  like  cows  (nie/gkais,  I  believe 
they  called  them)  that  destroyed  their  crops,  and  the  question 


RUDIMENTARY  NOTIONS  2J 

are  included  all  the  relations  between  the  terms 
of  propositions  assumed  as  premises,  whether 
upon  authority,  or  from  testimony,  or  other- 
wise, i.  e.,  between  the  terms  of  all  proposi- 
tions other  than  those  that  are  intuitively 
perceived  to  be  true,  or  that  are  inferred  from 
other  propositions. 

§  21.  THE  INFERRED  RELATIONS  OF 
TERMS. — The  inferred  relations  of  terms  in- 
clude all  relations  that  cannot  be  intuitively 
perceived  from  an  immediate  comparison  of 
the  terms,  or  that  are  not  assumed,  but  that 
can  be  inferred  by  comparing  the  given  terms 
respectively  with  a  third  or  middle  term,  the  re- 
lations of  which  to  the  given  terms  are  known. 
Thus,  e.  g.,  we  may  not  be  able  to  perceive 
from  a  mere  comparison  of  the  two  terms,  that 
"  Logic  is  a  branch  of  the  Science  of  Lan- 
guage," but  by  comparing  the  two  terms  of 
the  proposition  respectively  with  the  middle 

arose  whether  it  was  lawful  to  kill  them.  The  pundits  to 
whom  the  question  was  referred  were  of  the  opinion  that, 
though  not  cows,  the  animals  were  quasi-cows,  and  therefore 
not  to  be  killed.  The  term  will  be  found  to  be  of  equal 
utility  in  Logic  as  in  the  Law.  In  fact,  a  very  useful  book 
might  be  written  on  the  subject — that  might  be  appropriately 
termed  Quasics.  For,  outside  of  concrete  notions,  all  notions 
denoted  by  terms  are  formed  by  analogy  from  sensible  images, 
and  are  quasi-things  only,  as,  e.g.,  imagination,  reflection, 
perception,  etc.  We  suggest  the  term  Quasics  not  with  a  view 
of  seriously  recommending  it  for  common  use,  but  simply  for 
the  purpose  of  directing  attention  to  a  very  important  subject. 


28  LOGIC 

term,  "  The  Science  of  the  Term,  the  Proposi- 
tion, and  the  Syllogism, ' '  the  relation  of  species 
and  genus  between  the  subject  and  the  predi- 
cate will  be  at  once  perceived.  For"  Logic  is 
the  Science  of  the  Term,  the  Proposition,  and 
the  Syllogism,"  and  "  The  Science  of  the 
Term,  etc.,"  is  a  species  or  kind  of  "  the 
Science  of  Language,"  and  hence  "  Logic  is 
a  species  or  kind  (i.  e.,  a  branch)  of  the  Science 
of  Language."  And  so  we  may  not  be  able  to 
perceive  from  a  mere  comparison  of  the  terms 
that  "  the  Thracians  were  barbarians, "  but  by 
comparing  these  terms  with  the  middle  term, 
"  Not -Greeks,"  the  conclusion  is  apparent ;  for, 
ex  vi  termini,  all  "  Not-Grecks  "  were  barba- 
rians. So,  generally,  using  the  letters  X,  Y,  Z, 
etc.,  to  represent  the  terms  of  any  proposition, 
we  may  not  be  able  to  perceive  intuitively  the 
truth  of  the  proposition  that  Z  is  X,  yet,  if  it 
be  intuitively  perceived  or  assumed  that  Z  is 
Y,  and  that  Y  is  X,  we  may  infer  that  Z  is  X. 
§  22.  PROPOSITIONS  AND  SYLLOGISMS. — An 
immediate  relation  of  terms,  whether  intuitive 
or  assumed,  can  be  expressed  only  in  the  form 
of  a  proposition — which  may  be  defined  simply 
as  the  expression  of  such  a  relation ;  and  an 
inferred  relation,  only  in  the  form  of  three 
propositions  constituting  what  is  called  a  syllo- 
gism. The  proposition  may  be  expressed  in 
the  formula:  Y  is  X;  and  all  syllogisms  in  the 


RUDIMENTARY  NOTIONS  29 

formula:  Z  is  Y,  Y  is  X,  .  * .  Z  is  X;  or,  Z  is 

Y,  Y  is  not  X  .  •  .  Z  is  not  X— the  letters 
standing  for  terms  or  names,  and  the  three 
points  (.  *  .)  being  the  sign  of  illation,  and 
equivalent  to  the  expression,  "  ergo,"  or 
"  therefore."  ' 

§  23.  OF  APODICTIC  AND  DIALECTIC. — Ra- 
tiocination may  consist  wholly  of  judgments 
and  inferences,  or  partly  of  these  and  partly  of 
assumed  propositions.  In  the  former  case  it  is 
wholly  illative,  or  demonstrative;  in  the  latter, 

1  To  define  a  term  (as  indicated  in  the  etymology  of  defini- 
tion} is  in  effect  to  establish  the  boundaries  by  which  the  class 
of  significates  denoted  by  it  is  separated  from  all  other  things  ; 
and  these  boundaries  may  be  conveniently  represented  by 
circles  or  other  enclosed  figures.  These  are  known  as  Euler's 
symbols,  and  are  extremely  convenient  and  universally  used 
by  logicians.  A  universal  affirmative  proposition  is  expressed 
by  a  circle  contained  in  a  circle,  the  former  representing  the 
subject,  the  latter  the  predicate  ;  the  universal  negative  by 
two  circles  excluding  each  other  ;  and  the  syllogism,  by  thus 
expressing  its  several  propositions;  as,  c.  g. ,  in  the  following 
diagrams : 

Affirm.  Prop.  Neg.  Prop. 


©0 


Neg.  Syll. 


3O  LOGIC 

only  partially  so,  i.  e.,  only  so  far  as  the  valid- 
ity of  the  inference  is  concerned.  The  prin- 
ciples governing  the  former  kind  of  ratiocination 
constitute  what  is  called  Apodictic  ;  those  gov- 
erning the  latter,  Dialectic.  It  will  be  seen  as 
we  progress  that  Apodictic  is  far  more  extensive 
in  its  scope  or  use  than  is  commonly  supposed, 
and  that  it  includes,  in  fact,  not  only  the 
Mathematical  Sciences,  both  pure  and  applied, 
but  also  a  large  part  of  Morality,  Politics,  and 
Jurisprudence  generally.  And  especially,  it  is 
important  to  observe,  it  includes  the  subject 
of  our  present  investigations.  For  Logic, 
though  not  so  treated  by  modern  logicians,  is 
strictly  a  demonstrative  science,  and  will  be  so 
treated  in  this  essay.1 

§  24.  VALID  RATIOCINATION  ILLATIVE  IN 
NATURE. — All  ratiocination,  or  reasoning  ex- 
plicitly stated,  discloses  at  once  its  validity  or 
invalidity — that  is  to  say,  appears  on  its  face 
to  be  either  conclusive  in  its  effect,  or  fal- 
lacious. Hence,  all  ratiocination,  unless  fal- 
lacious, is  illative  or  conclusive,  or,  we  may 
say,  demonstrative  in  its  nature.  On  the  other 

1  One  of  the  most  universal  infirmities  of  the  average  mind 
is  an  incapacity  to  distinguish  (outside  the  mathematics)  be- 
tween mere  opinion  and  apodictic,  or  demonstrated  truth. 
With  regard  to  the  latter,  the  man  who  is  conscientious  and 
accurate  in  his  Logic  may  realize  the  fine  saying  of  Seneca : 
"  It  is  truly  great  to  have  in  one  the  frailty  of  a  man  and  the 
security  of  a  god  "  (cited  Bacon,  Essays,  "  Of  Adversity  "). 


RUDIMENTARY  NOTIONS  31 

hand,  unless  explicitly  stated,  no  reasoning, 
however  apparently  convincing,  can  be  re- 
garded as  of  this. nature.  Hence,  from  a  logi- 
cal point  of  view,  reasoning  in  general  may  be 
regarded  as  either  valid  (i.  e.,  illative),  or  as 
invalid;  the  latter  of  which  may  be  either  fal- 
lacious or  simply  inconsequent.  The  former 
may  be  appropriately  called  Logical  Reason- 
ing, the  latter  Non-logical  or  Rhetorical;  by 
which  is  meant  not  necessarily  illogical  or  fal- 
lacious, but  either  fallacious  or  simply  inconse- 
quent, i.  e.,  non-illative. 

§  25.  RIGHT  REASONING  DEFINED. — It  is 
with  the  former  only  that  Logic  is  directly  con- 
cerned, and  to  it  we  may  without  impropriety 
give  the  name  of  RigJit  Reasoning.  For  the 
logical  quality  of  the  reasoning  does  not  de- 
pend upon  the  truth  or  falsity  of  the  conclusion, 
but  upon  the  rectitude  of  the  definitions,  judg- 
ments, and  inferences. 

§  26.  LOGIC  THE  ART  OF  RIGHT  REASON- 
ING.—  Logic,  therefore,  regarded  as  an  art, 
may  be  simply  defined  as  the  Art  of  Right 
Reasoning;  and  it  must  therefore  be  regarded 
as  denoting  the  ultimate  test  or  criterion  of 
truth  or  error.  For  until  the  reasoning  is 
made  explicit,  it  cannot  be  determined  whether 
it  is  right  or  otherwise.  It  also  includes  the 
doctrine  of  Fallacy,  or  Wrong  Reasoning; 
but  as  the  latter  has  for  its  end  simply  the 


32  LOGIC 

avoidance  of  error,  as  a  means  of  assuring  the 
rectitude  of  our  reasoning,  it  may  be  regarded 
simply  as  one  of  the  practical  aspects  of  the 
doctrine  of  Right  Reasoning. 

§  27.  LOGIC  TO  BE  REGARDED  AS  INTEL- 
LECTUAL MORALITY. — Logic  must,  therefore, 
be  regarded  as  bearing  to  reasoning  the  same 
relation  as  Morality  to  conduct.  It  may, 
therefore,  be  appropriately  called  Intellectual 
Morality* 

1  Hence  it  is  that  Logic,  like  Morality,  is  not  popular  with 
those  who  disregard  its  precepts  ;  among  whom  are  to  be  in- 
cluded the  large  majority  of  writers,  and  especially  of  phil- 
osophers. The  principle  is  as  expressed  in  the  adage  : 

"  What  thief  e'er  felt  the  halter  draw 
With  good  opinion  of  the  Law  ?" 


CHAPTER  II 

DOCTRINE   OF   THE   TERM 

I 
OF    THE    NATURE    OF    THE    TERM 

§  28.  "  TERM,"  "  NAME,"  AND  "  WORD" 
DISTINGUISHED  AND  DEFINED. — These  words 
are  often  used  as  synonymous,  but  the  distinc- 
tion between  them  is  material  and  important. 
A  word  is  a  vocal  sign,  or  vocable,  express- 
ing a  thought,  or  a  thought  expressed  by  such 
a  sign.  Under  the  name  "  word  "  is  included 
the  substantive  or  noun,  and  also  other  parts  of 
speech,  as,  e.  g.,  the  article,  the  conjunction, 
etc.  A  name  (noun  or  substantive,  which  may 
be  either  simple  or  complex'}  is  a  word  or  set  of 
words  used  to  signify  an  object  of  thought  re- 
garded as  a  thing,  z.  i\,  as  an  existing  substance 
or  entity.  The  knowledge  or  cognition  of  a 
thing  by  the  mind  is  called  a  notion  or  concept ; 
hence  a  name  may  be  otherwise  denned  as  a 
word,  or  set  of  words,  expressing  a  notion,  or 
33 


34  LOGIC 

as  a  notion  thus  expressed.  A  notion  or  con- 
cept is  itself  a  thought,  but  it  differs  from 
other  thoughts  as  being  the  thought  of  a  thing, 
i.  e,,  of  something  as  existing.  A  term  is  a 
name  used  as  a  subject  or  predicate  of  a  pro- 
position. It  is  therefore  to  be  regarded  merely 
as  an  element  of  the  proposition ;  and  the  pro- 
position as  the  principal  subject  in  Logic. 

§29.  "THING"  DEFINED.  —  The  term 
thing  is  used  in  two  different  senses  that 
must  be  carefully  distinguished.  In  its  proper 
sense  the  term  denotes  an  actual  thing  or  sub- 
stance, whether  material  or  spiritual,  as,  e.  g., 
mineral,  vegetable,  animal,  gas,  man,  soul, 
God,  etc.  In  this  sense  things  constitute  the 
actual  universe,  and  all  notions  or  concepts 
whatever,  unless  false  or  unreal,  are  ultimately 
derived  from  them.  But,  in  another  sense, 
the  term  is  used  to  denote,  not  only  actual 
existences,  or,  as  we  may  call  them,  real  things, 
but  mere  objects  of  thought,  or  things  existing 
only  in  contemplation  of  mind,  and  to  which 
there  are,  in  fact,  no  real  things  directly  cor- 
responding.1 These  may  be  appropriately 

1  All  true  or  real  notions  must  correspond  to  real  or  actual 
things,  but  the  correspondence  may  be  either  direct  between 
the  notion  and  the  real  things  signified  by  the  term  —  as  in 
the  case  of  concrete  terms,  <?.  g.,  "  man,"  "  horse,"  etc.  ; 
or  indirect — as  in  the  case  of  abstract  terms  —  between  the 
notion  and  the  things  whose  attributes  are  signified.  Thus, 
taking  for  example  the  term  "  redness  ,"  there  is  apparently  a 


THE    TERM  35 

called  <7?/rt.$7- things;  and  of  this  kind  are  the 
concepts  or  notions  denoted  by  all  abstract 
terms;  which  denote,  not  real  things  or  in- 
dividuals, but  mere  abstractions,  as,  c.  g., 
such  terms  as  "  justice,"  "  the  state,"  the 
names  of  the  several  colors,  disease,  death, 
etc.  ;  where  the  things  denoted  are  not  actually 
existing  things,  but  mere  concepts  of  qualities 
or  attributes  of  things  objectified  by  the 
mind. 

§  30.  "  CONCEPT,"  "  NOTION,"  AND 
"THOUGHT"  DEFINED.— The  term  "  con- 
cept," or  "  notion,"  or  "  thought  "  (in  this 
connection  we  may  use  either  indifferently)  is 
a  relative  term  implying  or  connoting,  in  its 
strict  or  proper  sense,  an  individual  thinking 
mind  of  which  it  is  the  product;  and  hence 
the  term  will  have  a  different  meaning  accord- 
ing to  the  correlative  to  which  it  refers.  It 
must  therefore  have  many  different  senses;  of 
which  two  must  be  especially  distinguished. 
In  its  proper  sense  it  denotes  simply  a  certain 
affection  of  the  mind  of  the  individual;  and 
in  this  sense,  obviously,  it  is  momentary  and 
evanescent,— like  the  snow  falling  on  the  river, 
described  by  the  poet,  as  "  ae  moment  white, 

direct  correspondence  between  the  notion  expressed  and  the 
qttasi-\\\\ng  signified,  though  in  reality  they  are  the  same  ;  but 
there  is  an  indirect  real  correspondence  between  the  notion  of 
redness  and  the  red  things  of  which  it  is  a  quality. 


36  LOGIC 

then  gone  forever."  For  though,  it  is  said, 
the  thought  recurs  to  us,  it  is  not,  nor  can  it 
be,  the  same  thought,  but  is  merely  a  copy  or 
image  of  it.  So,  when  a  thought — as  it  is  said 
— recurs  to  us,  it  is  always,  or  at  least  almost 
always,  suggested  to  us  by  the  word  in  which 
it  is  embodied  ;  and,  as  to  us,  so  also  to  others. 
But  Logic  does  not  have  to  deal  with  the  mo- 
mentary, fleeting  thought  of  the  individual, 
but  with  the  thought  only  that  is  continuously, 
or  we  may  say  permanently  reproduced,  and 
communicated  by  one  to  another;  that  has  be- 
come incarnate  in  words,  and  is  thus,  even 
when  lost  from  the  mind,  at  once  preserved, 
and  continuously  suggested,  or  brought  back 
to  the  consciousness  of  each  and  all.  Hence, 
in  Logic,  the  terms,  notion,  concept,  and 
thought,  are  to  be  regarded  as  used  in  a 
secondary  or  derived  sense,  as  denoting  the 
common  notions,  concepts,  and  thoughts  of 
mankind  embodied  in  words.  Hence  the  things 
or  significates  denoted  by  abstract  and  other 
universal  terms  have  in  fact  a  kind  of  exist- 
ence outside  of  any  and  all  individual  minds; 
which,  as  opposed  to  substantial,  may  be  called 
logical  existence ;  i.  e.,  they  exist  in  the  word 
(logos],  and  their  existence  is  as  real  and  of 
precisely  the  same  nature  as  that  of  the  word 
of  which  they  are  an  essential  part.  Hence, 
though  we  speak  of  abstractions  as  fictitious 


THE    TERM  37 

(i.  c. ,  feigned)  or  imaginary  things,  yet  they 
are  real,  and  in  some  cases,  as,  e.  g.,  in  the 
case  of  death,  disease,  misery,  poverty,  etc., 
terribly  real  facts.  What  is  meant  by  the  term 
"fictitious  tiling  "  is,  not  that  the  notion  signi- 
fied is  false  or  unreal,  but  that,  for  logical  pur- 
poses, it  is  fictitiously  regarded  as  a  thing. 

§  31.  THE  NORMAL  LOGICAL  TERM.— 
Every  term  legitimate  for  logical  purposes, 
or  we  may  say  every  logical  term,  is  therefore 
to  be  regarded  as  involving  or  implying  three 
essential  notions  or  elements,  namely;  (i)  the 
vocal  sign,  or  vocable,  (2)  the  notion  denoted, 
and  (3)  the  actual  tilings,  or  objective  realities, 
to  which  the  notion  and  the  vocal  sign  are  sup- 
posed to  correspond.  These  are  all  to  be  re- 
garded as,  in  one  sense,  essential  elements  of 
the  logical  term.  For  though,  where  the  last 
is  lacking,  a  term  may  exist,  and  it  is,  there- 
fore, possible  to  have  an  absurd  or  nonsensical 
term,  yet  such  a  term  is  not  such  as  is  contem- 
plated when  we  regard  the  end  of  Logic ;  which 
is  not  to  deal  with  absurdities  or  ingenious 
puzzles,  but  to  discover  truth  and  avoid  error. 
Hence,  an  absurd  or  nonsensical  term,  or,  in 
other  words,  a  term  whose  signification  does 
not  correspond  to  reality,  is  not  the  normal  or 
true  term,  essential  to  legitimate  ratiocination; 
nor  is  Los[ic — unless  in  illustrating  some  of  its 

o  o 

formal  operations — in  any  way  concerned  with 


43331 


38  LOGIC 

it,  except  to  detect  and  expose  its  inherent 
vice  and  its  essential  insufficiency  for  logical 
purposes. 

§  32.  THE  DENOTATION  AND  CONNOTA- 
TION OF  TERMS. — All  terms  are  regarded  in 
Logic  as  denoting  or  signifying  classes  of  in- 
dividuals.1 The  individuals  constituting  the 
class  denoted  by  the  term  are  marked  or  dis- 
tinguished by  certain  common  attributes,  at 
once  common  and  peculiar  to  the  class,  as, 
e.  g.,  the  class  "  man  "  by  the  mark  ''rational," 
by  which  it  is  distinguished  from  other  kinds 
of  animals.  Accordingly  a  term  is  said  to 
denote  the  individuals  designated  by  it,  and  to 
connote  the  qualities  or  marks  by  which  the 
class  is  determined.  Thus,  e.  g.,  the  term 
"  man-"  denotes  the  class  of  animals  known  by 
that  name,  and  connotes  the  quality  or  attribute 
of  rationality  by  which  the  class  is  distin- 
guished. 

§  33.  THE  MEANING  AND  SIGNIFICATION 
OF  TERMS. — The  individuals  constituting  the 
class  denoted  by  a  term  are  said  to  be  signified 
by  the  term,  and  are  called  its  significates, 
Thus  the  term,  man,  denotes  the  class,  man, 
as  a  whole,  but  signifies  each  and  all  of  the  in- 
dividual men  composing  it.  The  significates 
of  a  term  may  be  real, — which  is  the  case  when 
they  are  real  individuals  or  things,  existing  in 

1  See  infra,  §  35. 


THE    TERM  39 

nature;  or  they  may  be  unreal,  or  fictitious, 
i.  e.,  existing  only  in  contemplation  of  mind; 
which  is  the  case  with  all  abstract  terms,  and 
with  concrete  terms  where  the  classes  of  indi- 
viduals denoted  are  fictitiously  regarded  as  in- 
dividuals,— as,  e.g.,  when  we  speak  of  "  man  " 
as  one  of  the  significates  of  "animal. "  When 
a  term  denotes  a  class  of  real  individuals  —  as, 
t\  g.,"  man,"  regarded  as  denoting  men  gener- 
ally— its  significates  are  real ;  when  it  denotes  a 
class  of  lower  classes— as,  e.  g. ,  the  several  races, 
Asiatics,  Europeans,  etc. —  they  are  unreal  or 
fictitious.  In  the  former  case  the  term  is  said 
to  denote  an  infima  species  ;  which  is  to  be  de- 
fined as  a  class  made  up  of  real  individuals. 
By  the  meaning  of  a  term  is  meant  both  its 
denotation,  or  signification,  and  its  connotation 
taken  together;  and  the  word  "  meaning" 
may  also  be  regarded  as  equivalent  to  notion 
or  concept. 

§  34.  THE  EXTENSION  AND  INTENSION  OF 
TERMS. — The  extension  of  a  term  corresponds 
to  its  denotation,  or  signification,  and  is  deter- 
mined by  the  extent  of  Ihe  class  denoted,  or 
by  the  number  of  significates  signified  by  it. 
The  intension  of  a  term  is  but  another  name 
for  its  connotation,  —  both  words  denoting 
merely  the  qualities  or  attributes,  or,  in  other 
words,  the  marks  by  which  the  class  is  deter- 
mined. 


40  LOGIC 

II 

OF    THE    SEVERAL    KINDS    OF    TERMS 

§  35.  SINGULAR,  AND  COMMON,  OR  UNI- 
VERSAL, TERMS.  —  Grammatically  speaking, 
terms  are  said  to  be  either  singular  or  common, 
or,  as  otherwise  expressed,  singular  or  uni- 
versal. A  singular  term  is  one  that  denotes 
an  individual  or  single  thing,  as,  e.  g. ,  any  par- 
ticular thing,  animal,  or  man.  A  common  or 
universal  term  is  one  that  denotes  either  a  class 
of  individuals  or  a  class  made  up  of  other 
classes.  But  in  the  latter  case,  the  subordinate 
classes  may  be  regarded  as  individuals  consti- 
tuting the  superior  class;  and  conversely  the 
individual  may  always  be  regarded  as  a  class,— 
/.  e.,  a  class  of  one.1  In  this  work,  therefore, 
the  distinction  between  singular  and  common 
or  universal  terms  will  be  regarded  as  logically 
immaterial ;  all  terms  will  be  regarded  as  uni- 
versals,  or,  in  other  words,  as  denoting  classes 
of  significates. 

§  36.  ADJECTIVES.— Hence  also  adjectives 
used  as  terms  will  be  regarded  as  nouns  or  sub- 

1  "  By  a  class  is  usually  meant  a  collection  of  individuals 
.  ;  but  in  this  work  the  meaning  of  the  term  will  be  ex- 
tended so  as  to  include  the  case  where  but  a  single  individual 
exists,  as  well  as  cases  denoted  by  the  terms  '  nothing'  and 
'  universe'1 ;  which  as  'classes'  should  be  understood  to  com- 
prise respectively  'no  beings'  and  'all  beings.'"  —  Boole, 
Laws  of  Thought,  p.  28. 


THE    TERM  •  41 

stantives;  that  is  to  say,  where  a  term  is  in 
adjective  form  (which  can  occur  only  with  the 
predicate)  it  is  either  regarded  as  a  substantive, 
or  converted  into  one  by  adding  the  substan- 
tive understood.  Thus,  e.g.,  the  proposition, 
"  Man  is  mortal,"  is  to  be  read:  "  Man  is  a 
mortal,"  or  "  a  mortal  being." 

§  37.  ABSTRACT  AND  CONCRETE  NAMES.— 
A  concrete  name  is  one  that  denotes  a  class  of 
real  individuals.  An  abstract  name  is  one  that 
denotes  qualities  or  attributes  conceived  as  ex- 
isting apart  from  the  things  in  which  they  in- 
here, or,  in  other  words,  fictitiously  regarded  as 
things, — as,  e.  g.,  whiteness,  strength,  goodness, 
humanity,  etc.'2  Abstract  names  are  commonly 
singular  in  form,  but  in  their  essential  nature 
they  are  always  universal.  Thus,  when  we 
speak  of  virtue,  the  name  is  to  be  regarded  as 

1  "  If  we  attach  to  the  adjective  the  universally  understood 
subject,  '  being  '  or  '  thing,'  it  becomes  virtually  a  substantive, 
and  may  for  all  the  essential  purposes  of  reasoning  be  replaced 
by  the  substantive.  Whether  or  not  in  every  particular  of  the 
mental  regard  it  is  the  same  thing  to  say,  '  water  is  a  fluid 
thing,'  as  to  say,  '  water  is  fluid,'  it  is  at  least  equivalent  in  the 
expression  of  the  processes  of  reasoning." — Boole,  Laws  of 
Thought,  p.  2J. 

'2  The  distinction  between  concrete  and  abstract  names  cor- 
responds precisely  to  the  distinction  made  by  old  logicians 
between  names  of  first  intention  and  names  of  second  inten- 
tion. The  former  are  names  that  denote  real  significates  ; 
the  latter,  names  that  denote  fictitious  significates,  or  quasi- 
things.  See  further  on  this  point  Appendix  I. 


42  LOGIC 

denoting,  not  a  quality  existing  in  any  par- 
ticular man,  or  in  itself,  but  the  class  of  quali- 
ties by  which  all  virtuous  men  are  distinguished. 
So,  though  we  may  consider  the  color  red,  or 
redness,  in  the  abstract, —  dismissing  from  the 
mind  the  individuals  in  which  it  is  manifested, 
—  yet,  upon  analyzing  the  concept,  we  cannot 
fail  to  perceive  that  there  are  as  many  individ- 
ual instances  of  red,  or,  we  may  say,  as  many 
individual  reds  or  rednesses,  as  there  are  indi- 
vidual things  in  which  the  color  is  manifested; 
and  that  red,  or  redness,  is  simply  the  denomi- 
nation of  the  class  of  colors  thus  manifested. 
Hence,  abstract  names,  though  grammatically 
singular,  are  to  be  regarded  as  plural,  and  as 
differing  from  concrete  names  only  in  this,  that 
the  individuals  constituting  the  class  are  quali- 
ties,— i.  e.,  quasi-  things,  or  fictitious,  not  actual 
existences, —  and  that  among  the  marks  by 
which  the  class  is  distinguished  are  the  actual 
individuals  in  whom  alone  the  qualities  exist. 
An  abstract  name  is  therefore  to  be  regarded 
as  denoting  a  class  of  qualities  ;  and  as  connoting 
the  individuals  in  which  they  inhere. 

§  38.  THE  DISTINCTION  OF  FUNDAMENTAL 
IMPORTANCE. —  The  distinction  between  con- 
crete and  abstract  names,  or  names  of  first,  and 
of  second  intention,  is  one  of  fundamental  im- 
portance. In  dealing  with  the  former,  the 
things  denoted  by  the  names  we  use  are  ever 


THE    TERM  43 

present  to  the  mind,  and  we  may  therefore,  as 
is  asserted  by  Mill,  be  said — without  violent 
absurdity  —  to  deal  with  things,  rather  than 
with  notions  or  names.  But  where  we  deal 
with  abstract  terms,  the  things  present  to  the 
mind  are  mere  abstractions,  fictitiously  re- 
garded as  things;  and  we  are,  in  fact,  dealing 
not  with  things,  but  with  ^^.yz-things  only.1 

§  39.  POSITIVE  AND  NEGATIVE  TERMS.— 
The  distinction  between  positive  and  negative 
terms  is  also  one  of  fundamental  importance 
in  Logic.  By  this  division  of  terms  the  whole 
universe  of  things,  real  and  fictitious,  is  divided 
into  two  classes,  the  one  marked  by  having, 
the  other  by  not  having,  a  certain  quality  or 
qualities,  as  e.  g.,  white  things,  and  things 
that  are  not  white ;  and  it  is  obvious  that  to 
each  positive  there  must  be  a  corresponding 
negative  term. 

§  40.  OF  THE  UNIVERSE  OF  THE  PROPOSI- 
TION.— But  ordinarily  in  speech  we  have  in 
view  a  more  limited  class,  and  must  be  under- 
stood to  refer,  not  to  the  universe  of  things, 
but  to  some  class  less  than  the  universe,  but 
superior  to  the  classes  denoted  by  the  subject 
and  predicate;  and  this  superior  class  is  said 
to  constitute  the  universe  of  the  proposition  in 
which  the  terms  are  used.  Thus,  when  we 
speak  of  "  mortal"  and  "  immortal,"  the  class 

1  See  Appendix  K. 


44 


LOGIC 


of  "  living  things"  or  "  beings"  is  obviously 
referred  to  as  the  superior  class,  and  is,  there- 
fore, said  to  constitute  the  universe  of  the 
proposition;  and  the  division  is  to  be  under- 
stood to  be  into  "  mortal"  and  "  immortal" 
beings.  So,  in  the  proposition,  "  Brutes  are 
irrational,"  the  superior  class  we  have  in  view 
is  that  of  animals,  and  this  class  is  to  be  re- 
garded as  the  universe  of  the  proposition ;  as 
(denoting  "  no t "  by  the  Greek  privative,  a] 
may  be  illustrated  by  the  following  diagrams, 
either  of  which  may  be  used : 


III 


OF    THE    ANALYSIS    OF    TERMS 

§41.  APPREHENSION. —  As  it  is  the  func- 
tion of  Logic  to  compare  the  notions  de- 
noted by  terms,  with  the  view  of  determining 
their  relations,  a  preliminary  process  is  essen- 
tial.  namely,  that  of  apprehending  or  under- 
standing the  significations  of  terms;  which  is 
called  by  logicians,  "  Simple  Apprehension." 

1  The  operations  of  the  mind  involved  in  reasoning  are  (i) 
Simple  Apprehension,  (2)  Judgment,  and  (3)  Inference  (see 


THE    TERM  45 

This  is  effected  by  means  of  what  may  be 
called  the  "  Analytical  Processes  ";  which  will 
next  be  considered. 

§42.  ANALYTICAL  PROCESSES. — As  pre- 
liminary to  apprehension,  it  is  essential  that 
the  sense  in  which  the  term  is  to  be  used  shall 
be  identified,  or,  in  other  words,  that  of  the 
several  senses  usually  denoted  by  a  vocable, 
one  shall  be  selected.  This  is  often  called 
nominal  definition  (i.  e. ,  definition  of  the  name), 
but  improperly;  for  until  it  is  determined  in 
what  sense  a  term  is  used,  there  is  in  fact  no 
name.  Hence  we  call  it,  Vocal  Definition,  i.  c., 
Definition  of  the  Vocable.  Next,  it  is  necessary, 
before  the  two  terms  can  be  compared,  to  ap- 
prehend, in  the  case  of  each  of  them,  the  sig- 
nificates  of  the  term,  or  the  class  of  significates 
denoted  by  it ;  for  otherwise  we  will  not  be 
able  to  compare  their  significations.  This  is 
effected  by  the  definition  of  the  term ;  which, 
to  distinguish  it  from  vocal,  is  called  nominal 
or  real  definition  1  ;  and  this  again  involves  the 
process  of  classification  or  division. 

Whately,  Logic],  I  have  altered  the  ordinary  statement  of 
these  operations  by  substituting  for  the  third  "Inference" 
instead  of  "Discourse";  which  is  commonly  defined  as 
"reasoning"  or  "ratiocination."  But,  as  used  in  this  work, 
these  words  include  both  Apprehension  and  Judgment. 

1  There  is  some  confusion  among  logicians  as  to  the  use  of 
the  terms,  Nominal  Definition  and  Real  Definition.  By  some, 
the  former  term  is  used  as  denoting  what  I  have  called  vocal 


46  LOGIC 

§  43.  VOCAL  DEFINITION. — A  word,  or  vo- 
cable,— i.  e. ,  the  vocal  sign, — has  usually  many 
significations;  and  commonly,  in  using  it,  we 
do  not,  at  first,  distinguish  between  such  of  the 
notions  denoted  by  it  as  are  nearly  the  same, 
but,  instead  of  regarding  it  (as  we  should)  as 
part  of  several  names,  use  it  as  though  it  were 
a  single  name.  But  in  thus  using  a  vocable 
without  distinguishing  its  several  senses,  it  is 
inevitable  that,  in  the  course  of  the  ratiocina- 
tion, it  will  be  used  in  a  shifting  sense,  or 
rather,  we  should  say,  in  several  senses,  as 
suggested  by  the  varying  occasion ;  and  that 
the  coherency  of  our  reasoning  will  thus  be 
destroyed.  This  fault  in  ratiocination  is  called 
the  fallacy  of  confusion  or  of  ambiguity,  and, 
as  will  be  seen  in  the  sequel,  is  one  of  the  most 
common  and  most  serious  of  fallacies.  Hence 
it  is  one  of  the  most  important  and  imperative 
of  logical  rules  that,  in  the  case  of  every  word 
we  have  occasion  to  use  in  our  reasoning,  the 
sense  in  which  it  is  to  be  used  shall  be  clearly 

definition  ;  but  this  seems  to  be  incorrect.  According  to  the 
better  usage,  a  Nominal  Definition  is  a  definition  of  the 
Notion  expressed  in  a  term  ;  and  hence  Whately  says  "  that 
Logic  is  concerned  with  nominal  definitions  only."  To  this 
Mansel  objects  on  the  ground  that  "  Logic  is  concerned  with 
real  or  notional  definitions  only  ;  its  object  being  to  produce 
distinctness  in  concepts,  which  are  the  things  of  Logic  "  (Man- 
sel's  Aldrich,  p.  39).  But  this  is  precisely  what  Whately 
means  ;  and  says. 


THE    TERM  47 

distinguished  and  consistently  observed.  And 
this  indeed,  ex  vi  termini,  is  essential  even  to 
the  beginning  of  ratiocination;  for,  until  this 
is  effected,  we  have  not  even  that  essential 
material  of  ratiocination,  a  name,  with  which 
to  deal.  The  vocal  definition  of  a  term  may 
be  effected  in  various  ways, — as,  e.  g.,  by  the 
use  of  any  other  term,  or  phrase,  or  sentence 
of  equivalent  signification ;  or,  negatively,  by 
rejecting  those  senses  of  the  word  that  we  do 
not  wish  to  use;  or,  often,  by  an  imperfect 
definition,  as  by  simply  specifying  the  genus  of 
the  class  denoted  by  the  term  ;  or,  in  fine,  by 
any  means  that  may  serve  to  confine  the  term 
to  one  sense  only,  and  thus  to  prevent  am- 
biguity. 

§  44.  DIVISION  AND  CLASSIFICATION.  - 
Division  consists  in  distributing  the  class  of 
significates  denoted  by  a  name  into  subordinate 
classes,  with  appropriate  names;  classification 
in  the  reverse  process  of  assigning  a  class  de- 
noted by  a  name  to  a  class  denoted  by  another 
name. 

§  45.  GENUS  AND  SPECIES. — In  the  former 
case,  the  class  distributed  is  called  the  genus ; 
the  classes  into  which  it  is  distributed,  species, 
In  the  latter,  the  class  assigned  is  a  species,  the 
class  to  which  it  is  assigned,  the  genus.  The 
genus  and  species,  however,  as  in  the  case  of 
synonyms,  may  be  of  equal  extension. 


48  LOGIC 

§  46.  DIVISION. — Division  is  an  act  of  Anal- 
ysis ;  Classification,  of  Synthesis.  But  the 
same  principles  govern  both,  and  the  elucida- 
tion of  one  will  equally  explain  the  other.  In 
Logic,  the  analysis  of  terms  is  the  more  im- 
portant process,  and  we  will  therefore  adopt, 
as  the  subject  of  explanation,  the  process  of 
Division.  The  term  to  be  divided,  or,  rather, 
the  class  denoted  by  the  term,  is,  as  we  have 
said,  called  the  genus;  the  subordinate  classes 
into  which  the  genus  is  divided,  species.  The 
species  must,  of  course,  be  exclusive  of  each 
other, — i.  e.,  they  must  not  overlap;  and  taken 
together  they  must  exhaust  the  genus.  Thus, 
the  term  thing — meaning  thereby  things  and 
quasi-things — may  be  divided,  and  subordinate 
classes  subdivided,  as  follows: 

Things 


Real  Things     Ouasi-Things 


Bodies     Not  Bodies 


Organic     Inorganic 


Animal     Not  Animal 


Rational       Not  Rational 
etc. 


§  47.    DICHOTOMY.  —  It   will   be   observed 
that  the  above  division  is,  in  each  case,  two- 


THE    TERM  49 

fold, — i.  e.j  into  two  classes,  represented  by 
a  term  and  its  negative.  This  is  called  Dichot- 
omy, and,  as  in  using  it  we  are  less  liable  to 
error  than  in  other  modes  of  division,  it  is 
most  commonly  used.  The  genus  may,  how- 
ever, be  divided  into  three  or  more  species,  pro- 
vided the  species  taken  together  exhaust  the 
genus,  and  be  exclusive  of  each  other, —  as,  e. 
g.,  in  the  division  of  Bodies  into  (i)  Inorganic, 
(2)  Vegetable,  and  (3)  Animal. 

§  48.  NOMINAL  DEFINITION  OF  TERMS.— 
The  definition  (/.  e.,  the  real  or  nominal  defini- 
tion) of  a  term  consists  in  assigning  the  class 
denoted  by  it  to  an  appropriate  genus,  and 
giving  its  specific  difference  ;  by  which  is  meant 
some  mark  or  marks  peculiar  to  it,  by  which  it 
may  be  distinguished  from  other  species.  It 
is,  therefore,  a  species  of  classification, — i.  e., 
it  consists  simply  in  classifying  the  given  class, 
or  species,  by  assigning  it  to  a  genus,  and  in 
adding  also  the  appropriate  marks,  or  specific 
difference,  by  which  it  is  distinguished  from  the 
other  species  contained  in  the  genus.  The 
definition  of  a  term  is,  therefore,  to  be  regarded 
simply  as  a  complete  classification  of  it;  and 
the  classification  of  it  as  an  incomplete  or  im- 
perfect definition.  But  the  latter  has  the  ad- 
vantage that  it  can  often  be  used  where  the 
former  would  be  inconvenient  or  impossible. 

§49.    THE   ESSENCE  OF  THE  TERM. — A 


50  LOGIC 

quality  at  once  common  and  peculiar  to  the  in- 
dividuals denoted  by  a  term  is  called  a  property 
of  the  class  denoted ;  a  quality  common  to  the 
class,  but  not  peculiar  to  it,  is  called  an  acci- 
dent* The  definition  of  a  term  is  made  up  by 
selecting  from  the  accidents  of  the  term  one  to 
serve  as  a  mark  for  the  purpose  of  determining 
the  genus,  and  from  the  properties  one  to  serve 
as  specific  difference.  These  together  constitute 
the  essence  of  the  term ;  which  will  therefore 
vary  with  the  definition,  and  be  determined  by 
it.  Thus,  e.  g.,  if  we  define  man  as  a  rational 
animal,  "animal"  will  be  the  genus;  ra- 
tional" the  specific  difference;  "talking',"' 
laughing, "  "  cooking, ' '  etc. ,  properties  ;  ' '  mor- 
tal," "  carnivorous,"  "  mammal,"  etc.,  acci- 
dents. But  we  may,  if  we  choose,  define  him 
variously  as  a  talking,  laughing,  or  cooking, 
mortal,  carnivore,  or  mammal.  The  essence  of 
a  term  is  therefore  but  another  name  for  the 
meaning  of  the  term.  Properties  not  used  for 
specific  difference,  and  accidents  not  used  for 
genus,  do  not  enter  into  the  essence  of  the  term. 

1  There  is  much  confusion  among  logicians  in  the  use  of  the 
term  accident.  The  definition  in  the  text  is  that  of  the  best 
authorities,  including  Aristotle  ;  and  the  term  should  be  con- 
sistently thus  used. 


CHAPTER    III 

DOCTRINE   OF   THE    PROPOSITION 

I 
RUDIMENTS    OF    THE    DOCTRINE 

§  50.  PROPOSITION  DEFINED. — A  proposi- 
tion may  be  defined  as  the  expression  of  a  rela- 
tion of  signification  between  two  terms;  which, 
of  course,  implies  the  expression  of  the  corre- 
sponding relation  between  the  notions  ex- 
pressed in  the  terms. 

§51.  THE  GRAMMATICAL  PROPOSITION.— 
But  here  there  is  a  difference  between  Logic 
and  Grammar,  or,  we  may  say,  between  the 
logical  and  the  grammatical  proposition.  In 
the  latter,  any  of  the  innumerable  relations  ex- 
isting between  terms,  or,  what  is  the  same 
thing,  between  the  things  denoted  by  them, 
'whether  past,  present,  or  future,  may  be  ex- 
pressed as  existing  between  the  terms;  and  the 
relation  may  be  expressed  by  any  copula  or 
connecting  word,  or  the  same  word  may  be 
51 


52  LOGIC 

used  to  express  both  copula  and  predicate,  as, 
e.  g.,  "  John  struck  William  "  ;  "  The  sun  will 
rise  at  six  o'clock  to-morrow";  "  It  rains"; 
"  The  Carthaginians  did  not  conquer  Rome," 
etc.  But  in  Logic  the  only  copula  used  is  the 
present  tense  of  the  verb  "  to  be"  with  or 
without  the  negative  particle  ;  and  the  only  in- 
terterminal  relation  considered  is  that  of  species 
and  genus;  which  may  be  either  affirmed  or 
denied. 

§  52.  THE  LOGICAL  PROPOSITION. —  Ac- 
cordingly the  logical  proposition  is  of  two 
forms,  the  affirmative  and  the  negative.  In 
the  former  the  relation  of  species  and  genus 
between  the  terms  is  affirmed, — as,  e.  g. ,  "  Man 
is  mortal,"  '  Y  is  X,"  etc.  ;  in  the  latter  it  is 
denied, — as,  e.  g. ,  "  Man  is  not  perfect,"  '  Y 
is  not  X,"  etc.  The  affirmative  proposition 
may  be  read,  either,  "  Y  is  X,"  or  "  Every  Y 
is  X,"  or  "  All  Y's  are  X's  "  ;  or,  to  take  the 
concrete  example,  '  Man  is  mortal,"  or 
"  Every  man  is  mortal,"  or  "  All  men  are 
mortal," — these  expressions  being  all  equiva- 
lent, and  signifying  equally  that  the  subject 
class — or  class  denoted  by  the  subject  —  is  a 
species  of  the  predicate  class.  The  negative 
proposition  may  be  read  either  as  above  or  as' 
follows:  "  No  man  is  perfect,"  '  No  Y  is  X," 
etc.  It  is  a  cardinal  postulate  in  Logic  that  all 
propositions  may,  and  indeed  —  for  purposes 


THE  PROPOSITION  53 

of  logical  analysis  —  must  be  converted  into 
logical  form;  as,  e.  g.,  the  above  examples 
into  the  following  :  "  John  is  the  man  who 
struck  William  "  ;  "  Six  o'clock  is  the  hour  at 
which  the  sun  will  rise  to-morrow";  "  Rain 
is  falling";  "  The  Carthaginians  are  not  [or, 
grammatically,  we  should  say,  "  were  not  "] 
the  conquerors  of  Rome."  ' 

§  53.  INTERPRETATION  OF  THE  LOGICAL 
PROPOSITION. — In  all  logical  propositions  the 
copula  is  to  be  interpreted  as  meaning  "  is  con- 
tained in  "  or  "  is  a  species  of,"  or  the  contrary, 
as  the  case  may  be.2  Hence  in  Logic  the  only 

1  There  are  commonly  recognized  by  logicians  four  forms  of 
the  proposition,  designated  respectively  by  the  letters,  A,  E, 
I,  and  O,  and  called  the  "  Universal  Affirmative"  the  "Uni- 
versal Negative"    the    "Particular   Affirmative"    and    the 
"Particular    Negative"    (see    infra,    §88).      But    if    in     I 
and  O  we  regard   the   expression    "some    Y" — instead    of 
"  Y  " — as  the  subject  of  the  proposition,  these  forms  will  be- 
come the  same  as  A  and  E.     Hence,  propositions  may,  as  in 
the  text,  be  regarded  as  of  two  kinds  only,  namely,  affirma- 
tive and  negative ;  the   former  affirming  that  the  subject  is 
included  in  the  predicate  class  ;   the  latter  denying  that  it  is  so 
included.      This  distinction  agrees  precisely  with  our  defini- 
tion,  and  will   be   sufficient    for  our   present   purposes,   and, 
indeed,  for  all  practical  purposes. 

2  The  affirmative  proposition  "  Y  is  X  "  is  to  be  construed  as 
asserting  that  the  class  Y  is  wholly  included  in  the  class  X  ;  the 
negative,  "  Y  is  not  X,"  that  it  is  wholly  excluded.     But  the 
class  Y  may  denote  a  part  of  a  class,  as,  e.  g. ,  "  Some  A  "  ; 
in  which  case  the  proposition  "  Y  is  X,"  or  "  Y  is  not  X," 
would  be  equivalent  to  the  ordinary  forms,  "Some  A  is  X." 
or  "  Some  A  is  not  X," 


54  LOGIC 

significative  relation  recognized  is  the  relation 
of  the  inclusion  or  exclusion  of  the  subject 
class  in  or  from  the  predicate:  and  accordingly 
this  may  be  called  appropriately  the  logical 
relation.  Yet  the  logical  proposition  is  not  less 
capacious  of  expression  than  the  grammatical ; 
for,  as  the  latter  may  always  be  converted  into 
the  former,  it  follows  that  all  relations  may  be 
expressed  in  the  one  as  in  the  other.  The 
only  difference  is  that  in  the  grammatical  prop- 
osition the  relations  between  the  notions  in- 
volved may  be  expressed  either  in  the  copula, 
or  in  the  terms  themselves ;  while  in  the  logical 
proposition  the  only  interterminal  relation  ex- 
pressed (i.  e.y  affirmed  or  denied)  by  the  copula 
is  that  of  species  and  genus,  and  all  other  re- 
lations between  notions  are  expressed  in  the 
terms,  —  i.  e.,  in  complex  terms.1 

§  54.  THE  CONVERSION  OF  PROPOSITIONS. 
— By  conversion  is  meant  the  transposition  of 
subject  and  predicate — i.  e.,  making  the  predi- 
cate the  subject,  and  the  subject,  predicate. 
But,  such  conversion,  to  be  legitimate,  must  be 
illative,  /.  e.,  the  force  or  conclusiveness  of  the 
proposition  must  not  be  affected.  Thus  the 
proposition,  "  Y  is  not  X  "  (since  the  subject  and 
predicate  classes  are  mutually  exclusive),  may 
be  converted  into  the  proposition,  "  X  is  not 

1  This  is  admirably  illustrated  by  Mr.  Boole's  system  of 
signs,  of  which  I  append  an  epitome.  See  Appendix  L. 


THE  PROPOSITION  55 

Y,"  which  is  called  simple  conversion;  and  so 
with  all  definitions,  and  other  equational  proo- 
ositions;  and  also  with  the  particular  affirma- 
.tive  proposition,  "  Some  Y  is  X."  But  the 
affirmative  proposition,  "  Y  is  X,"  cannot  be 
thus  simply  converted;  for  the  subject  class  is 
identical  with  only  "  some  "  of  the  predicate 
class,  and  in  conversion  the  predicate  must  be 
qualified  by  that  particle,  thus  substituting  a 
new  term.  Or,  symbolically,  the  proposition, 
'  Y  is  X,"  can  be  converted  only  into  the 
proposition,  "  Some  X  is  Y  ";  which  is  called 
conversion  per  accidens. 

II 

SEVERAL    THEORIES    OF    PREDICATION 

§  55.  THE  COPULA. — In  the  logical  proposi- 
tion, as  we  have  seen,  the  copula  is  interpreted 
as  meaning  "is  contained  in,"  or  the  contrary- 
and  this  is  the  traditional,  or,  as  it  may  be 
called,  orthodox,  theory  of  predication.  But 
the  copula  may  be  otherwise  interpreted ;  and 
from  these  several  interpretations  several  theo- 
ries of  predication  will  result.  Of  these,  two 
may  be  distinguished  as  requiring  some  remark, 
namely,  the  Equational  Theory,  in  which  the 
copula  is  interpreted  as  meaning,  "  is  equiva- 
lent to,"  and  is  expressed  by  the  sign  of  equiv- 
alence (=) ;  and  the  Intensive  Theory,  where  it 


56  LOGIC 

is  interpreted  as  meaning,  "  has  the  quality  or 
attribute"  Thus,  e.  g. ,  the  proposition,  "  Man 
is  rational,"  is  interpreted  according  to  the 
Traditional  Theory  as  meaning,  "  the  class 
man  is  contained  in  the  class  rational" ;  ac- 
cording to  the  Equational  Theory,  as  meaning, 

the  class  man  is  the  same  as  the  class 
rational" ;  and  according  to  the  Intensive,  as 
meaning,  "  the  individuals  constituting  the 
class  man  have  the  quality  or  attribute,  rational, 
or  of  rationality." 

§  56.  THE  EQUATIONAL  THEORY.— In  the 
logical  proposition,  the  classes  denoted  by  the 
subject  and  predicate  may  be  equal ;  for,  where 
this  is  the  case,  each  may  be  said  to  be  con- 
tained in  the  other.  Hence  in  such  cases  the 
proposition  is  always  convertible,  as,  e,  g,,  we 
may  say  indifferently  that  "  man  is  a  rational 
animal,'1  or  that  "a  rational  animal  is  a  man," 
or,  generally,  if  Y  =  X,  either  that  "  Y  is  X  " 
or  "X  is  Y."  Such  propositions  are  recog- 
nized and  used  in  the  traditional  Logic,  as  in 
the  case  of  definitions,  and  in  other  cases, 
but  it  is  not  thought  necessary  to  express  the 
equivalence  of  the  terms.  Hence  in  the  affirm- 
ative proposition  "  Y  is  X  "  it  cannot  be  deter- 
mined from  the  form  of  the  proposition  whether 
X  is  of  greater  extension  than  Y,  or  of  the 
same  extension. 

§  57.  QUANTIFICATION  OF  THE  PREDICATE. 


THE  PROPOSITION  .          57 

—The  modern  doctrine  of  "  the  quantification 
of  the  predicate  "  has  for  its  object  to  remedy 
this  supposed  defect  by  expressing  in  every 
proposition  by  an  appropriate  sign  the  quan- 
tity of  the  predicate,  or,  in  other  words,  by  in- 
dicating whether  it  is  distributed  or  not '  ;  and 
this  is  effected  by  prefixing  to  the  predicate  a 
sign  indicating  the  relation  of  quantity  between 
it  and  the  subject,  and  giving  to  the  propo- 
sition an  equational  form.  Thus,  e.  g.,  the 
proposition,  "  Y  is  X,"  may  be  expressed  in 
the  form  "  Y  =  vX,"  which  is  the  method  of 
Boole;  or  in  the  form  Y  =  YX,"  which  is 
the  form  proposed  by  Jevons,  and  is  read, 
"  Y  =  the  part  of  X  that  is  Y,"  or  "  the  Y's 
are  the  X's  that  are  also  Y's."  Or,  more  sim- 
ply, instead  of  the  proposition,  "  Y  is  X,"  we 
may  say,  "  Y  is  a  certain  species  of  X  "  ;  or, 
to  take  a  concrete  example,  instead  of  the 
proposition,  "  Man  is  an  animal,"  we  may  say, 

'  Man  is  a  certain  species  or  kind  of  animal." 
Hence,  whether  an  equational  proposition  shall 
be  expressed  in  the  traditional  or  in  the  equa- 
tional form  is  a  matter  of  choice  to  be 
determined  by  convenience.  Generally  the 

1  A  term  is  said  to  be  "  distributed"  when  it  is  taken  uni- 
versally, i.  e.,  where  the  other  term  of  the  proposition  is,  or 
may  be,  predicated  of  all  the  individuals  denoted  by  it,  as,  e.g., 
the  subject  of  a  universal  affirmative,  or  either  subject  or 
predicate  of  a  universal  negative  proposition  (see  ^  87). 


58       .  LOGIC 

traditional  form  is  sufficient,  as  we  can  readily 
determine  from  the  matter  of  the  proposition 
whether  it  is  to  be  regarded  as  equational  or 
otherwise.  But  in  the  mathematics  the  equa- 
tional form  is  much  the  more  efficient,  and  is 
therefore  always  used. 

§  58.  THE  INTENSIVE  THEORY. — The  differ- 
ence between  the  traditional  and  the  intensive 
theory  of  predication  is  that,  in  construing  the 
proposition,  we  have  regard  in  the  former  to 
the  extension  of  the  terms  only ;  but  in  the 
latter,  in  construing  the  predicate,  we  have  re- 
gard to  its  intension.  Thus,  when  we  say  "  Man 
is  mortal,"  we  mean,  in  the  former  case,  that 
the  class  man  is  contained  in  the  class  mortal ; 
but  in  the  latter,  that  man  has  the  quality  or 
attribute  of  mortality.  But  the  latter  expres- 
sion means  nothing  more  than  that  "  the  qual- 
ity of  mortality  is  contained  in,  or  among,  the 
qualities  of  man  ";  which  is  itself  an  extensive 
proposition.  Hence  the  intensive  interpreta- 
tion of  the  proposition  simply  results  in  an 
extensive  proposition  in  which  the  qualities 
of  the  original  terms  are  substituted  for  its 
original  significates,  and  the  terms  inverted. 
Thus,  e.g.,  if  we  denote  by  Y'  the  qualities  of 
Y,  and  by  X'  the  qualities  of  X,  the  proposi- 
tion, Y  is  X,  may  be  converted  into  X'  is  Y'; 
which  may  be  called  Intensive  Conversion,  or 
conversion  by  Intensive  Interpretation. 


THE  PROPOSITION  59 

§  59.  TRADITIONAL  THEORY  OF  PREDICA- 
TION.— Even  under  this  theory  the  proposition 
seems  to  be  susceptible  of  several  interpreta- 
tions. Thus,  e.  g.,  we  have  interpreted  the 
copula  as  meaning  "  is  contained  in  or  "  is  a 
species  of  "  ;  and  again  we  may  interpret  it  as 
meaning  that  the  significates  constituting  the 
subject  class  may  each  and  all  be  called  by  the 
name  constituting  the  predicate  —  or,  in  other 
words,  that  the  name  predicated  belongs  to 
the  significates  of  the  subject  term,  or  of  any  of 
them ;  which  has  been  called  interpreting  the 
judgment  "in  its  denomination  "  (Thompson's 
Laws  of  Thought,  §  195).  But  for  all  logical 
purposes  these  interpretations  are  practically 
the  same,  and  it  will  make  no  difference  whether 
the  proposition  be  interpreted  in  the  one  way 
or  the  other.  This  is  sufficiently  obvious  with 
regard  to  the  expressions,  "  is  contained  in," 
and  "  is  a  species  of  "  ;  and  is  equally  true  of 
the  interpretation  suggested  by  Dr.  Thompson. 
For,  taking  as  an  example  the  proposition, 

'  Man  is  an  animal,"  it  is  obviously  indifferent 
whether  we  construe  it  as  meaning  "  the  class 
man  is  included  in  the  class  animal"  or  that 

'  it  is  a  species  of  the  class  animal,"  or  that 
"  the  name  animal  is  applicable  to  all  signifi- 
cates of  the  name  man."  These  varieties  of 
interpretation  will,  therefore,  not  demand  a 
further  consideration. 


DO  LOGIC 

§  60.  COLLECTIVE  AND  DISTRIBUTIVE  IN- 
TERPRETATION.— There  is,  however,  another 
difference  of  interpretation  it  is  important  to 
consider;  and  especially  with  reference  to 
mathematical  reasoning,  which  is  to  be  con- 
sidered presently.  Common  terms,  or  terms 
denoting  classes  of  more  than  one,  may  be  used 
either  collectively  or  distributively, —  i.  e.,  the 
class  denoted  by  the  term  may  be  regarded 
either  as  a  whole  made  up  of  individuals,1  or  as 
a  number  of  individuals  constituting  a  class,  or 
signified  by  the  name.  Thus,  e.  g.,  the  term 
"  man  "  may  be  used  to  denote  either  the  class 
"  man,"  as  when  we  say,  "Man  is  mortal"; 
or  the  individuals  composing  the  class,  as 
when  we  say,  "  A  man  is  a  mortal,"  or  "  Men 
are  mortals."  Whether  a  term  is  used  collec- 
tively or  distributively  may  be  indicated,  as  in 
the  above  examples,  by  the  expression,  or  may 
be  simply  understood  ;  or  the  expression  may  be 
such  as  not  to  indicate  either  expressly  or  im- 
plicitly whether  the  term  is  used  in  the  one  way 
or  the  other.  With  regard  to  the  subject  of  the 
proposition  it  is  logically  immaterial  in  which 
way  the  term  is  used.  Thus,  in  the  proposi- 
tion, "  Y  is  X, "  the  subject  is  used  collectively ; 
and  in  the  proposition,  "  All  Y's  are  X's,"  or 

1  When  a  concrete  term  is  construed  collectively,  it  becomes 
abstract,  and  is  to  be  regarded  as  denoting,  not  a  number  of 
real  individuals,  but  one  quasi  individual  only. 


THE  PROPOSITION  6 1 

'  Every  Y  is  an  X,"  or  "A  Y  is  an  X,"  distri- 
butively ;  but  the  forms  are  logically  equivalent. 
So  with  regard  to  the  predicate,  where  the 
terms  are  of  equal  extension,  it  is  immaterial 
whether  it  be  construed  collectively  or  distribu- 
tively,  provided,  if  the  predicate  be  construed 
collectively,  that  the  subject  also  be  thus  con- 
strued. For  to  construe  a  term  collectively  is 
to  regard  the  class  denoted  by  it  as  an  individ- 
ual, and  a  term  thus  construed  is  therefore  to 
be  regarded  as  a  singular  term.  But  a  singular 
term  cannot  be  predicated  of  any  but  a  singu- 
lar term,  with  which  it  must  exactly  conform 
in  signification;  or,  in  other  words,  a  singular 
term  can  be  predicated  of  another  singular  term 
only  in  the  equational  proposition.  Thus, 
e.  g.,  in  the  proposition,  "  Y  is  X,"  it  is  im- 
material whether  we  regard  Y  as  denoting  the 
class  Y,  or  as  signifying  the  significates  com- 
posing the  class.  But  the  class  X  cannot  be 
construed  collectively  unless  we  also  construe 
the  class  Y  in  the  same  way,  and  unless  also 
the  two  classes  are  co-extensive,  or,  in  other 
words,  unless  the  proposition  can  be  put  in  the 
form,  Y  =  X. 

Ill 

OF    THE    PREDICABLES 

§  61.  DEFINITION  AND  DIVISION  OF  THE 
PREDICABLES. — A  predicable  may  be  defined 


62  LOGIC 

as  a  term  that  may  be  made  the  predicate  of  an 
affirmative  proposition.  As  explained  above, 
such  propositions  may  be  either  equational  or 
non-equational.  In  the  former  case  the  predi- 
cate is  of  the  same  extension  as  the  subject ;  in 
the  latter,  of  greater  extension.  All  predi- 
cables,  therefore,  may  be  divided  into  two 
classes, — namely,  those  that  are  equivalent  to 
the  subject,  and  those  that  are  not  equivalent. 
An  equivalent  predicable  may  be  either  defini- 
tion or  property ;  for  each  of  these  is  precisely 
co-extensive  with  the  subject  (§  49).  Non- 
equivalent  predicables  must  be  either  genera 
or  accidents ;  either  of  which  may  always  be 
predicated  of  the  subject  (/#.).  This  is  the 
division  of  predicables  used  by  Aristotle. 

§62.  TWOFOLD  DIVISION  OF  PREDICABLES. 
—But  the  distinction  between  "  definition  "  and 
"  property  "  seems,  with  relation  to  the  subject 
of  predicables,  to  be  unimportant;  for  "prop- 
erty" differs  from  "definition"  only  in  the 
use  made  of  the  former  (/#.).  And  so  with 
reference  to  the  distinction  between  genus  and 
accident  (/#.).  Hence  it  has  been  proposed 
to  abandon,  as  at  least  unnecessary  for  logical 
purposes"  (or  rather,  we  should  say,  for  pur- 
poses of  predication),  "the  distinctions  between 
property  and  definition,  genus  and  accident, 
and  to  form,  as  Aristotle  has  also  done,  two 
classes  of  predicables ;  one  of  predicables  taken 


THE  PROPOSITION  63 

distributively  and  capable  of  becoming  subjects 
in  their  respective  judgments  without  limita- 
tion ;  the  other  of  such  as  have  a  different  ex- 
tension. In  the  former  the  predicable  has  the 
same  objects  [2.  e. ,  significates]  as  the  subjects, 
but  different  marks,  or  a  different  way  of  rep- 
resenting the  marks.  In  the  latter  there  is  a 
difference,  both  in  the  marks  and  the  objects  " 
(Thompson's  Laius  of  Thought,  §  69.)' 

§  63.  ONE  KIND  OF  PREDICABLES  ONLY.— 
But  even  the  twofold  division  of  predicables, 
into  equivalent  and  non-equivalent,  is,  from  the 
traditional  standpoint,  of  minor  importance; 
for,  as  we  have  seen,  the  old  Logic  ordinarily 
takes  no  account  of  equational  propositions, 
but  these,  like  others,  are  regarded  as  import- 
ing simply  the  inclusion  of  the  subject  in  the 
predicate;  and  in  this  mode  of  interpreting 
the  proposition,  we  have,  in  effect,  a  complete 
doctrine  of  the  predicables. 

1  The  division  of  predicables  most  commonly  used  is  that  of 
Porphyry  (Aristotle's  Logical  Treatises,  Bohn's  edition,  Intro- 
duction of  Porphyry  ;  also  Jevons's  Lessons  in  Logic,  p.  98). 
According  to  this  division,  " Specific  Difference"  is  substituted 
for  the  "  Definition  "  of  Aristotle's  division,  and  there  is  added 
as  a  fifth  predicable,  "  Species ,"  as  being  predicable  of  individ- 
uals. But,  as  observed  by  Mansel  (Aldrich's  Logic,  Preface), 
"whether  this  classification  is  an  improvement,  or  is  consist- 
ent with  the  Aristotelian  doctrine,  admits  of  considerable 
question."  The  view  taken  in  the  text  is  in  every  respect 
preferable  (Thompson's  Laws  of  Thought,  pp.  136  et  seq.). 


64  LOGIC 

IV 
OF    THE    RELATIONS    BETWEEN    TERMS 

§  64.  OF  THE  RELATIONS  OF  TERMS  GEN- 
ERALLY.— The  end  of  Logic  is  to  determine 
the  relations,  and,  as  involved  in  this,  the  defi- 
nitions, of  terms,  or  (what  is  the  same  thing), 
of  the  notions  expressed  in  terms  (§  16).  Of 
these  notions,  the  most  conspicuous  are  those 
existing  between  what  are  called  relative  words 
— as,  e.  g.,  father  and  son,  wife  and  husband, 
higher  and  lower,  etc.,  and  also  the  active 
and  passive  forms  of  the  verb,  and  all  in- 
flections of  verb  or  noun,  or,  in  a  word,  all 
paronyms,  etc.  But  the  term,  relative,  though 
applicable,  is  not  peculiar  to  this  class  of 
words,  and  is,  therefore,  not  altogether  appro- 
priate. Relations,  more  or  less  apparent,  exist 
between  all  terms,  and  in  the  development 
of  these  consists  the  raison  d'etre  of  Logic. 
Hence,  properly  speaking,  no  term  can  be  said 
to  be  absolute,  as  opposed  to  relative.  For — 
to  consider  only  one  of  the  most  general  of  re- 
lations—  any  thing,  or  class  of  things  (real  or 
fictitious),  must  always  be  assignable  to  one  of 
two  classes,  namely  the  class  denoted  by  a 
given  term,  or  to  the  class  denoted  by  its 
negative  '  ;  and,  in  addition  to  this  universal 

1  This,  of  course,  is  true  only  on  the  assumption  that  we 
reject  Particular  Propositions,  as  proposed  (§  52,  note). 


THE  PROPOSITION  65 

relation,  there  are  numerous  others,  either  of  a 
general  character, — as  e.  g.,  the  relation  be- 
tween numbers,  or  other  expressions  of  quan- 
tity,— or  such  as  are  peculiar  to  certain  words, 
— as,  e.g.,  between  hunger  and  animal,  hunger 
and  edible,  gravity  and  body,  fish  and  water, 
the  sun  and  the  planets,  etc.  In  fine,  the  re- 
lations between  terms  are  innumerable,  and, 
when  the  significations  of  terms  are  appre- 
hended, these  relations  may,  in  general,  or,  at 
least,  in  innumerable  cases,  be  either  intui- 
tively perceived,  or  demonstratively  inferred. 

§  65.  OF  THE  SEVERAL  KINDS  OF  INTER- 
TERMINAL  RELATIONS.  —  The  relations  of 
terms  are,  for  various  purposes,  divided  in  so 
many  different  ways  that  it  would  be  impracti- 
cable to  enumerate  them.  But,  of  these  divi- 
sions, there  are  three  that,  either  on  account  of 
their  intrinsic  importance,  or  of  the  importance 
attributed  to  them  by  logicians,  will  require 
our  attention.  These  consist  in  the  distinction 
made  (i)  between  the  Predicables  and  the  Cate- 
gories or  Predicaments  ;  (2)  between  the  formal 
and  the  material  relations  of  terms  ;  and  (3)  be- 
tween the  relations  that  are  intuitively  per- 
ceived, and  those  that  are  not,  or,  more  briefly, 
between  judgments  and  assumptions  (§19,  20). 

§  66.  (i)  OF  THE  PREDICABLES  AND  OF  THE 

Otherwise  we  would  fall  into  the  same  fallacy  as  Jevons  and 
Hobbes  (v.,  infra,  §  90  and  note). 
5 


66  LOGIC 

CATEGORIES  OR  PREDICAMENTS. —  The  dis- 
tinction between  these  corresponds  precisely  to 
the  distinction  we  have  made  between  the 
logical  and  the  grammatical  forms  of  the  prop- 
osition. Etymologically  both  terms  are  of  the 
same  import, — denoting  simply  terms  that  may 
be  predicated  of  other  terms,  i.  e. ,  that  may  be 
made  predicates  of  propositions;  but,  according 
to  inveterate  use,  the  former  term  relates  ex- 
clusively to  the  logical  proposition,  the  latter, 
to  the  grammatical.  There  is,  therefore,  an 
essential  difference  between  the  Doctrine  of 
the  predicables  and  that  of  the  Categories 
or  predicaments.  The  former  —  which  treats 
simply  of  the  relation  of  species  and  genus  be- 
tween the  terms  expressed  in  the  logical  prop- 
osition —  has  already  been  considered.  The 
latter  treats  of  all  the  various  relations  that 
may  exist  between  the  terms  of  the  grammati- 
cal proposition ;  and,  as  these  include  all  rela- 
tions, whatever,  that  may  exist  between  terms, 
or  between  their  significates,  it  follows  that  the 
categories  or  predicaments  are  to  be  understood 
as  denoting  the  most  general  classes  into  which 
such  relations  may  be  distributed.  By  such  a 
classification — if  it  could  be  accomplished — all 
relations  between  terms  and  between  things 
would  be  developed,  and  thus  a  basis  furnished 
for  a  classification  of  all  possible  predicates. 
But  the  subject  is  one  of  difficulty,  and  in  the 


THE   PROPOSITION  6/ 

present  state  of  philosophy,  a  satisfactory  treat- 
ment of  it  is  impracticable.  It  would  simply 
serve,  therefore,  to  confuse  the  student,  if  we 
should  enter  upon  it,  and  we  will  accordingly 
omit  it. 

§  67.  (2)  OF  THE  FORMAL  AND  OF  THE  MA- 
TERIAL RELATIONS  OF  TERMS. — By  informal 
relations  of  terms  are  meant  those  relations  that 
are  universal  in  their  nature, —  i.  e.,  that  exist 
generally  with  reference  to  all  terms;  as,  e.  g. , 
the  relation  between  terms  and  their  contra- 
dictories, between  a  term  used  universally  and 
the  same  term  used  particularly,  between  the 
subject  and  the  predicate  of  the  proposition, 
etc.  These  are  all  apparent  at  once  from  the 
mere  expression,  without  taking  note  of  the 
matter  of  the  term,  except  in  so  far  as  it  is 
universal  or  common  to  all  terms.  Thus,  e.  g., 
in  the  expression  "  not-man  "  we  perceive  at 
once  a  formal  relation  between  this  term  and 
"  man,"  and  in  this  case  the  privative  "  not," 
though  part  of  the  matter  of  the  term  not- 
man,  is  the  ground  of  the  relation;  which  is 
formal  because  universal.  And  so,  in  the 
terms  "  Y  "  and  "  some  Y,"  a  formal  relation 
is  apparent,  though  the  word  "  some  "  is  in  fact 
part  of  the  matter  of  the  term  "  some  Y." 

Hence,  the  distinction  between  the  formal 
and  the  material  relations  of  terms  does  not, 
as  is  commonly  supposed,  rest  upon  the 


68  LOGIC 

distinction  that,  in  the  former  case,  the  matter 
of  the  term  is  not  considered,  and,  in  the  latter, 
that  it  is ;  but  on  the  distinction  that  the  formal 
relations  are  based  upon  such  part  of  the  mat- 
ter or  meaning  of  terms  as  is  common  to  all  or 
to  many  terms,  and  with  that  regard  to  the 
material  relations  this  is  not  the  case. 

Hence,  logically,  there  is,  in  fact,  no  essential 
difference  of  nature  between  the  two  kinds  of 
relation.  For  the  material  relations  between 
terms  are  as  apparent  and  as  certain  as  the  so- 
called  formal  relations, — as,  c.  g,,  the  relations 
between  relative  terms,  as  "  father  "  and  "  son," 
etc.,  or  those  between  such  terms  as  "  island  " 
and  "continent,"  "island"  and  "water," 
"body"  and  "weight,"  "five"  and  "seven," 
"  nine  "  and  "  fifteen,"  etc. ;  and  they  differ  only 
in  this,  that  these  subsist  only  in  particular 
cases,  and  not  universally.  Hence  the  notion 
that  would  restrict  the  functions  of  Logic  to  the 
merely  formal  relations  of  terms  is  based  upon 
an  unessential  difference  of  nature  between 
these  and  other  relations,  and  therefore  cannot 
be  sustained. 

§  68.  (3)  OF  JUDGMENTS  AND  ASSUMPTIONS. 
— Of  the  immediate  relations  between  terms 
some  —  as  we  have  seen  —  are  self-evident,  or 
may  be  intuitively  perceived ;  others  are  not 
of  this  character.  Where  the  relation  between 
the  terms  of  a  proposition  is  of  the  former 


THE  PROPOSITION  69 

kind,  it  is  called  %.  judgment ;  where  the  rela- 
tion expressed  is  of  the  latter  kind  (if  not 
an  inference)  it  is  called  an  assumption  (§§ 
19  et  seq,}.  This  division  of  propositions  is 
based  upon  an  essential  difference  of  nature, 
and  is  one  of  fundamental  importance.  It 
will  therefore  require  our  most  attentive  con- 
sideration. 

LOGICAL  JUDGMENT  DEFINED. — In  the  logi- 
cal proposition,  the  only  relation  between 
the  terms  expressed  is  what  we  have  called 
the  significative  relation, — i.  e.,  the  relation 
of  inclusion  or  exclusion  of  one  of  the  terms 
in  or  from  the  other.  Hence  judgment,  in 
the  logical  sense,  may  be  defined  as  consist- 
ing in  the  intuitive  perception  of  a  significative 
relation  between  two  terms, — i.  e. ,  in  the  in- 
tuitive perception  that  the  subject  class  is,  or 
is  not,  included  in  the  predicate  class,  —  as, 
c.  g.,  where,  from  our  knowledge  of  the  signi- 
fication of  the  terms,  we  affirm  that  "  man  is 
an  animal, ' '  or  that  ' '  fishes  are  denizens  of  the 
water,"  or  that  "  bodies  are  affected  by  grav- 
ity," or  that  "  fortitude  is  the  only  resource 
against  the  inevitable,"  or,  in  the  Latin, 
"  Quidquid  crit  super anda  omnis  fortuna  ferendo 
est." 

§  69.  OF  THE  DISTINCTION  BETWEEN 
JUDGMENT  AND  ASSUMPTION. — The  product 
of  this  mental  process  —  as  we  have  seen  —  is 


7<D  LOGIC 

called  a  judgment ;  which  may  be  defined  as 
a  proposition  at  once  self-evident,  and  not  in- 
ferred from  another  proposition  or  proposi- 
tions. Hence,  the  opinion  that  "  propositions 
are  judgments  expressed  in  words"  is  a  de- 
parture from  the  logical  definition  of  a  judg- 
ment. A  judgment  expressed  in  words  is  a 
proposition,  but  the  converse  is  not  true.  For 
where  a  proposition  is  based  not  merely  upon 
a  comparison  of  its  terms,  or  upon  an  inference, 
but  upon  extrinsic  evidence,  or  authority,  or 
other  grounds,  the  forming  of  an  opinion  is 
not  a  logical  process,  and  the  proposition,  from 
a  logical  point  of  view,  is  to  be  regarded, 
not  as  a  judgment,  but  merely  as  an  assump- 
tion or  hypothesis.  Of  this  kind  is  the  prop- 
osition that  Pompey's  army  was  defeated  at 
Pharsalia;  that  Cicero  was  murdered  by  the 
Triumvirate  ;  that  a  given  policy  as,  e.  g., 
protection  to  home  industries,  or  the  remon- 
etization  of  silver,  will  be  beneficial,  etc. 

§  70.  OF  THE  DISTINCTION  BETWEEN 
APODICTIC  AND  DIALECTIC  (§  23).  —  Hence 
it  may  be  readily  perceived  how  inadequate 
is  the  conception  of  Logic  that  would  re- 
strict its  functions  to  merely  fornial  infer- 
ence to  the  exclusion  of  judgments;  or  the 
conception  of  demonstrative  or  apodictic  rea- 
soning that  would  confine  it  to  the  mathe- 
matics :  or  to  the  limited  class  of  sciences  that 


THE  PROPOSITION  71 

rest  upon  intuitions,  in  the  sense  of  the  term 
used  by  modern  metaphysicians ;  or  that  would 
exclude  from  it  all  reasoning  originating  in 
judgments  involving  empirical  notions  or  con- 
cepts. For,  logically,  a  judgment  as  to  a  sig- 
nificative relation  between  two  terms  denoting 
notions  or  concepts,  of  which  the  apprehension 
is  empirical, —  as,  e.  g.,  the  judgment  that 

bodies  are  affected  by  gravity,"  that  "  fish 
live  in  water,"  that  "  food  will  assuage 
hunger,"  etc., — is  quite  as  self-evident  as  the 
judgment  that  "  two  and  three  are  five,"  or 
that"  sixty-four  is  the  square  of  eight."  In 
fact,  the  two  classes  of  judgments  are,  logi- 
cally, of  precisely  the  same  nature,  —  each 
being  but  an  intuitive  perception  of  a  relation 
between  the  significations  of  two  terms;  as 
follows  from  our  definition. 

§  71.  No  DISTINCTION  IN  LOGIC  BETWEEN 
A  PRIORI  AND  EMPIRICAL  NOTIONS. — Logic, 
therefore,  takes  no  account  of  the  metaphysical 
distinction  between  a  priori  and  empirical  no- 
tions, but  regards  all  judgments  as  intuitive. 
Its  function  is  simply  to  determine  the  relations 
existing  between  the  significations  of  terms; 
and  if  the  significations  of  the  terms  com- 
pared be  apprehended,  and  be  of  such  nature 
that  the  relation  between  them  can  be  per- 
ceived, either  immediately — i.  e.  intuitively, 
— or  by  intermediary  comparison  with  other 


72  LOGIC 

terms,  the  conclusion  reached  —  which  ex- 
presses merely  the  relation  between  the  signi- 
fications of  the  terms  —  is,  so  far,  absolutely 
true. 

§  72.  OF  THE  ERROR  THAT  RATIOCINATION 
is  ONLY  HYPOTHETICALLY  TRUE.— Hence 
it  is  an  error  to  suppose  that  ratiocination  is 
only  hypothetically  true,  or,  in  other  words, 
that  Logic  is  not  concerned  \vith  the  truth  of 
premises.  In  many  cases  this  is  so;  but  it  is 
true  in  no  case  in  which  the  ratiocination  pro- 
ceeds from  judgments  exclusively.  For  in  all 
such  cases  the  premises  —  which,  as  we  have 
said,  merely  express  significative  relations  be- 
tween their  terms  —  are  not  merely  assumed, 
but  are  intuitively  known  to  be  true,  and  the 
conclusion  is  true,  not  hypothetically  but  ab- 
solutely. 

And  this  is  essentially  the  case  even  where 
the  notions  involved  in  the  original  judgments 
or  premises  are  themselves  false  or  unreal;  for 
the  ratiocination  has  for  its  direct  object  only 
to  determine  correctly  the  relation  between 
the  significations  of  the  terms  of  the  con- 
clusion ;  and  all  that  is  directly  asserted  in 
the  conclusion  is  that  the  signification  of  the 
terms  are  related  as  expressed  ;  and  hence, 
when  the  ratiocinative  functions  have  been 
rightly  performed,  the  conclusion  must  be 
necessarily  true.  But  as  it  is  necessary  for 


THE  PROPOSITION  73 

purposes  of  ratiocination  that  grammatical 
propositions  be  converted  into  logical,  so  also, 
for  practical  use  or  application,  all  logical  con- 
clusions must  be  reconverted  into  grammatical 
propositions,  or,  in  other  words,  construed  as 
asserting  not  merely  the  significative  relation 
expressed,  but  also  the  truth  or  reality  of  the 
notions  or  concepts  denoted  by  the  terms;  and 
when  thus  construed  the  conclusion  cannot  be 
regarded  as  being  absolutely  true,  unless  the 
terms  express  real  notions.  Hence,  it  may  be 
said  that  the  conclusions  reached  in  ratiocina- 
tion proceeding  exclusively  from  judgments 
are,  when  construed  grammatically,  true  only 
upon  the  hypothesis  that  the  notions  involved 
in  the  original  judgments  or  premises  are  true 
or  real,  and  hence,  that  such  conclusions  are 
true  absolutely  only  as  logically  construed. 
Thus,  e.  g.,  the  judgment  that  "  all  bodies 
are  affected  by  gravity"  is  intuitive;  but  of 
the  truth  or  reality  of  the  notions  expressed 
by  these  terms,  respectively,  we  have  no  as- 
surance but  experience.  And  from  these  ob- 
servations it  may  be  perceived  how,  and  in 
what  sense,  it  is  that  Politics,  Morality,  and 
the  Science  of  Human  Nature  generally  are 
all  to  a  large  extent  susceptible  of  demonstra- 
tion, and  to  that  extent  apodictic  in  their  nature 
(§§  23  et  seq.\ 


CHAPTER  IV 

DOCTRINE   OF   THE    SYLLOGISM 

I 
RUDIMENTS    OF    THE    DOCTRINE 

§  73.  ELEMENTS  OF  THE  SYLLOGISM. — The 
Syllogism  consists  of  three  propositions  (§  22): 
of  which  two  are  called  the  premises,  and  the 
other  the  conclusion.  It  has  also  three  terms. 
Of.  these,  two  appear  as  the  subject  and  the 
predicate  of  the  conclusion,  and  are  called, 
respectively,  the  minor  and  the  major  term. 
The  other — which  is  called  the  middle  tenn- 
is used  in  both  premises:  in  the  one  with  the 
major,  in  the  other  with  the  minor  term.  The 
premise  containing  the  major  term  is  called 
the  major,  and  that  containing  the  minor,  the 
minor  premise.  Thus  in  the  syllogism,  Y  is 
X,  Z  is  Y,  .'.  Z  is  X,"  Z  is  the  minor,  X  the 
major,  and  Y  the  middle  term ;  and  the  first 
proposition  the  major,  and  the  second  the 
minor  premise. 

74 


THE    SYLLOGISM  75 

§  74.  ANALYSIS  OF  THE  SYLLOGISM. — The 
proposition  is  but  the  expression  of  a  signifi- 
cative relation  between  its  terms.  Hence  the 
premises  of  a  syllogism  are  merely  statements 
of  the  significative  relations  of  the  terms  of 
the  conclusion  (the  major  and  the  minor)  re- 
spectively with  the  middle  term  ;  and  the 
conclusion  the  significative  relation  thereby 
inferred  between  its  terms.  The  essential  ele- 
ments of  the  process  consist,  therefore,  in  the 
comparison  of  the  two  terms  of  the  conclusion 
respectively  with  the  third,  or  middle  term, 
and  in  inferring  a  direct  relation  between  them. 

§  75.  DEFINITION  OF  THE  SYLLOGISM.— 
Hence  syllogistic  inference  may  be  more 
specifically  defined  as  consisting  in  the  infer- 
ence of  a  significative  relation  between  two 
terms  from  their  known  significative  relations 
to  a  third  term  with  which  they  are  respectively 
compared.1 

§  76.  THE  PRINCIPLE  OF  THE  SYLLOGISM. 
—The  principle  of  the  syllogism  (by  which  is 
meant  the  principle  or  axiom  on  which  de- 
pends the  illative  force  or  conclusiveness  of 
syllogistic  inference)  is  expressed  in  the  Dictum 
of  Aristotle,  or,  as  it  is  technically  called,  the 

1  The  definition  in  the  text  is  taken  substantially  from  that 
of  De  Morgan  ;  who  defines  the  syllogism  as  "the  inference 
of  the  relation  of  two  names  from  the  relation  of  each  of  those 
names  to  a  third"  (Formal  Log.,  p.  176). 


76  LOGIC 

Dictum  de  Omni  et  Nullo.  It  is  variously 
stated  by  logicians,  but  the  several  forms  are 
all,  in  effect,  identical.  Its  best  expression  is 
as  follows : 

DICTUM  DE  OMNI  ET  NULLO. — "Where 
three  terms  (which  we  will  call  the  middle 
and  the  two  extremes]  so  subsist  with  re- 
lation to  each  other  that  the  one  extreme  is 
contained  in  the  middle,  and  the  middle  is 
contained  in  [or  excluded  froni\  the  other  ex- 
treme, then  [as  the  case  may  be]  the  extreme 
included  in  the  middle  will  be  included  in  [or 
excluded  front}  the  other  extreme."  Where 
the  predication  is  affirmative  the  principle  is 
called  the  Dictum  de  Omni ;  where  negative, 
the  Dictum  de  Nullo. 

Omitting  in  the  form  given  above  the  words 
in  brackets,  it  becomes  the  Dictum  de  Omni ; 
substituting  the  words  in  brackets,  marked  as 
quoted,  for  the  corresponding  expressions,  it 
becomes  the  Dictum  de  Nullo. 

The  two  forms  of  the  Dictum  (affirmative 
and  negative)  correspond  precisely  to  the  two 
forms  of  syllogisms  called  Barbara  and  Cela- 
rent?  viz.  : 

1  This  is  substantially  the  form  given  to  the  Dictum  by 
Aristotle,  Prior  Analytics,  i.,  iv. 

*  Forms  of  the  Syllogism.  There  are  nineteen  forms  of 
valid  syllogisms  recognized  by  logicians,  which  are  explained 
in  the  next  chapter.  But  if  we  reject  the  use  of  particular 
propositions  (§  52  n.)  all  may  be  reduced  to  the  two  forms 


THE   SYLLOGISM  77 

Y  is  X  Y  is  not  X 

Z  is  Y  Z  is  Y 

.'.  Z  is  X  .'.  Z  is  not  X 

II 

THE    PRINCIPLE    OF    SUBSTITUTION 

§  77.  RULES  OF  INFERENCE. — The  follow- 
ing practical  rules  may  be  deduced  from  the 
Dictum  : 

(1)  In  any  affirmative    proposition  we  may 
always  (without  affecting  its  illative  force   or 
conclusiveness)  substitute  for  the  subject  any 
other  term  denoting  the  same,  or  part  of  the 
same,  significates;  and  for  the  predicate  any 
term  denoting  the  same  significates,  or  a  class 
that  contains  them. 

Or,  more  briefly,  we  may  always  in  the  sub- 
ject substitute  species  for  genus ;  and  in  the 
predicate,  genus  for  species. 

(2)  So,  in  any  negative  proposition,  we  may, 
without  affecting  its  illative  force,  substitute 
for  either  subject  or  predicate  any  term  denot- 
ing the  same,  or  part  of  the  same,  significates. 

Or,  more  briefly,  we  may  always,  in  the 
negative  proposition,  either  in  the  subject  or 
the  predicate,  substitute  species  for  genus. 

above  given,  which  are  called  Barbara  and  Celarent.  In 
these  forms  the  several  terms  may  be  represented  indifferently 
by  any  letters  ;  and  the  order  of  the  propositions  is  imma- 
terial. In  the  traditional  Logic  the  order  of  the  propositions 
is  always  as  in  the  examples  given  in  the  text. 


78  LOGIC 

(3)  To  which  may  be  added  the  following: 
In  any  affirmative  proposition  we  may  always 
substitute  for  the  predicate  any  other  term  that 
denotes  the  same  significates  as  the  subject,  or 
a  class  containing  them.1 

§  78.  EQUIVALENCE  OF  TERMS  DEFINED. 
—In  the  above  rules,  it  will  be  observed,  the 
term  substituted  is  not  necessarily  equivalent 
in  signification  to  the  term  for  which  it  is  sub- 
stituted;  but  it  is  equivalent  so  far  as  the 
force  of  the  inference  is  concerned,  or,  as  the 
lawyers  say,  quoad  the  argument.  It  may  be 
said,  therefore,  briefly,  that  mediate,  or  syllo- 
gistic inference  consists  simply  in  substituting 
for  the  terms  of  propositions  other  terms  equiv- 
alent in  ratiocinative  value. 

§  79.  CONVERSIONS  OF  PROPOSITIONS.— 
The  case  of  conversion  of  propositions  seems 
indeed,  to  be  an  exception ;  for  here  the  pro- 
cess seems  to  consist,  not  in  the  substitution 
of  terms,  but  in  the  substitution  of  a  new 

1  The  deduction  of  these  rules  from  the  Dictum  is  perhaps 
sufficiently  obvious,  but  as  it  may  not  be  apparent  to  all,  we 
subjoin  the  demonstration  : 

In  the  first  syllogism  (Barbara)  it  will  be  perceived,  as  ex- 
pressed in  the  minor  premise,  that  Z  is  a  species,  and  X  the 
genus,  of  Y,  and  that  the  conclusion  is  arrived  at  by  substitu- 
ting for  Y,  in  the  major  premise,  its  species  Z  ;  or,  for  Y  in  the 
minor  premise,  its  genus  X. 

In  the  latter  syllogism  (Celarent)  the  process  consists  in  sub- 
stituting for  Y,  in  the  major  premise,  its  species  Z  ;  and  so  it 
is  obvious  we  may  substitute  for  X  in  the  major  premise  any 


THE    SYLLOGISM 


79 


proposition  containing  the  same  terms  as  the 
original  with  the  order  of  terms  transposed. 
But  the  exception,  in  the  case  of  negative  and 
equational  propositions,  is  more  apparent  than 
real ;  for  the  two  forms  of  the  proposition  (i.  e., 
the  converted  and  the  original  proposition)  are 
precisely  the  same  in  effect,  and  there  is,  in 
fact,  neither  term  nor  proposition  substituted. 
For  when  we  say  "  Y  is  not  X,"  we  equally 
and  as  explicitly  say  "  X  is  not  Y  "  — the  mean- 
ing of  either  proposition  being  simply  that  the 
two  classes  denoted  by  X  and  Y  are  mutually 
exclusive;  and  so  in  the  equational  proposition 
(Y  =  X)  we  say,  in  the  same  breath,  both  that 
Y  is  equal  to  X,  and  that  X  is  equal  to  Y.  So, 

species  of  the  genus  X,  as,  e.  g.,  A,  B,  or  C,  and  thus  con- 
clude that  "  Z  is  not  A,  B,  or  C  "  (as  the  case  may  be)  ;  as  may 
be  illustrated  by  appropriate  diagrams  : 


So,  in  the  major  premise  in  Barbara,  we  may  substitute  for 
X  the  expression  YX,  or  any  species  of  X  containing  Y,  as, 
e.  g.,  A,  and  thus  conclude  that  Z  is  YX,  or  Z  is  A,  as  the 
case  may  be. 


8O  LOGIC 

upon  consideration,  it  will  be  found  that  the 
conversion  of  the  (universal)  affirmative  propo- 
sition— i.  e.,  conversion  per  accidens — is  not  an 
exception  to  the  rule,  but  an  application  of  it; 
for  the  process  consists  simply  in  substituting 
for  the  predicate  another  term  precisely  equiv- 
alent to  the  subject  in  signification,  as,  e.  g., 
in  the  proposition  Y  is  X,"  the  expression 
"  some  X"  for  "  X,"  —meaning,  by  the  ex- 
pression "  some  X,"  that  part  of  X  which  co- 
incides with  Y;  which  is  but  an  application  of 
Rule  3.  And  when  this  substitution  is  made, 
the  proposition  becomes  equational,  and  means 
the  same  thing  whether  we  convert  it  or 
not. 

§  80.  OF  IMMEDIATE  INFERENCES  GENER- 
ALLY.— Propositions  derived  from  other  propo- 
sitions by  conversion,  and  also  those  derived 
by  opposition  (explained  infra,  §  89),  are  re- 
garded by  recent  logicians  as  inferences,  and 
to  distinguish  them  from  syllogistic  inferences 
are  called  immediate.  This  innovation  we  re- 
gard as  unfortunate,  though  of  too  general  use 
to  be  neglected,  for,  according  to  our  view, 
only  one  kind  of  inference  is  allowed,  namely, 
syllogistic.  This,  as  we  have  shown,  includes 
the  case  of  conversion  per  accidens  ;  and  it  also 
includes  other,  and  perhaps  all,  cases  of  so- 
called  immediate  inference ;  as  may  be  readily 
shown. 


THE    SYLLOGISM  8 1 

(i)  SUBSTITUTION  OF  CONTRADICTORY. — 
One  of  these  is  what  is  called  by  Bishop 
Thompson,  "  Immediate  Inference  by  Means 
of  Privative  Conceptions"  and  by  other  logi- 
cians, improperly,  " Infinitation"  It  is,  in  fact, 
identical  with  the  process  treated  hereafter 
under  the  head  of  "  Conversion  by  Contrapo- 
sition "  (§  91).  It  consists  in  substituting  for 
the  predicate  its  negative,  or  contradictory,  and 
in  changing  the  quality  of  the  proposition, — 
i.  e.,  making  the  copula  of  the  negative  propo- 
sition affirmative,  or  that  of 'the  affirmative 
proposition  negative.  Thus,  denoting  the 
terms  by  the  capital  letters  Y  and  X,  and  their 
negatives  or  contradictories  by  aY  and  aX, 
the  negative  proposition  "  Y  is  not  X  "  may  be 
converted  into  the  affirmative  proposition,  "  Y 
is  aX  "  ;  and  similarly  the  affirmative  proposi- 
tion, "  Y  is  X,"  into  the  negative  proposition, 
"  Y  is  not  aX  "  (i.  e.,  is  not  Not-X).  The 
validity  of  the  process,  as  may  be  illustrated 
by  the  following  diagrams,  rests  upon  the  prin- 
ciple that  any  negative  proposition,  as,  e.  g., 
"  Y  is  not  X,"  may  always  be  regarded  either 
as  denying  that  the  class  Y  is  included  in  the 
class  X,  or  as  affirming  that  it  is  included  in 
the  class  aX,  or  "Not-X";  and  conversely 
the  affirmative  proposition,  "  Y  is  X,"  may 
be  regarded  either  as  affirming  that  the 
class  Y  is  included  in  the  class  X,  or  as 


82 


LOGIC 


denying  that  it  is   included   in   the  class  aX, 
Not-X." 


or 


But  when  from  the  affirmative  proposition 
'  Y  is  X  "  we  conclude  that  "  Y  is  not  Not- 
X,"  there  is  a  syllogistic  inference;  which,  de- 
noting the  negative  or  contradictory  of  X  by 
aX,  may  be  thus  expressed : 

X  is  not  aX  (/.  e.,  not  Not-X) 
Yis  X 

.*.  Y  is  not  aX. 

The  inference,  therefore,  rests  upon  the 
judgment  that  the  term  "  X  "  is  equivalent  to 
the  term  "  Not-aX,"  and  consists  in  substi- 
tuting the  latter  for  the  former.  Hence  the 
principle  of  inference  involved  may  be  stated 
generally  by  saying  that  a  term  is  always 
equivalent  in  signification  to  the  contradictory 
of  its  contradictory,  or,  as  otherwise  expressed, 
the  negative  of  its  negative ;  which  is  but  a 
different  expression  of  the  maxim  that  "  two 
negatives  make  an  affirmative." 

It  is,  indeed,  said  that  the  major  terms  in  the 
two  propositions  are  the  same — the  proposi- 
tions differing  only  in  quantity,  and  hence 


THE   SYLLOGISM  83 

that  no  third  term  is  introduced.  But  this  is 
incorrect ;  for  the  major  term  in  the  former 
proposition  is  X,  and  in  the  latter  "  not 
Not-X  "  ;  and  it  is  a  fundamental  logical  doc- 
trine that  no  two  terms  are  identical  that  differ, 
.either  in  denotation  or  connotation,  or  vocal 
sign ;  and  also  that  the  very  essence  of  ratio- 
cination consists  in  the  recognition  of  identity 
of  signification  in  terms  having  different  con- 
notations or  vocal  signs,  and  in  the  substitution 
of  the  one  for  the  other  (§§  77  et  seg.}. 

(2)  IMMEDIATE  INFERENCE  BY  ADDED  DE- 
TERMINANTS, AND  (3)  THE  SAME  BY  COMPLEX 
CONCEPTIONS. — These  kinds  of  supposed  im- 
mediate inference  were  introduced  into  Logic 
by  Leibnitz  (Davis,  Theory  of  Thought ;,  p.  104). 
The  former  is  stated  in  the  proposition  that  the 
same  mark  may  be  added  to  both  terms  of  a 
judgment;  the  latter,  in  the  proposition  that 
the  two  terms  of  a  judgment  may  be  added  to 
the  same  mark.  Of  the  former,  the  example 
given  by  Thompson  is:  "A  negro  is  a  fellow- 
creature,"  therefore,  "  A  negro  in  suffering  is 
a  fellow-creature  in  suffering  "  ;  of  the  latter: 
"  Oxygen  is  an  element,"  and  therefore,  "  The 
decomposition  of  oxygen  would  be  the  decom- 
position of  an  element."  The  two  processes 
seem  to  be  in  substance  the  same,  and  both 
may  be  expressed  symbolically  by  saying  that 
"  If  Y  is  X,"  then"  ZY  will  be  ZX,"  or  (what 


84  LOGIC 

is  the  same)  "  YZ  will  be  YX  "  '  ;  as  may  be 
thus  symbolically  illustrated: 


This  process  is  erroneously  regarded  by  logi- 
cians as  an  immediate  inference;  but  it  is,  in 
fact,  mediate,  and  may  be  stated  in  syllogistic 
form  as  follows : 

Y  is  X 

ZY  is  Y 

.'.  ZY  is  X 

The  conclusion  "  ZY  is  X,"  fully  expressed, 
is  that  ZY  is  that  part  of  X  with  which  it  co- 
incides ;  or,  in  other  words,  that  "  ZY  is  ZYX." 
But  ZYX  is  ZX;  and  hence  ZY  is  ZX. 

In  this  case  the  observations  made  with 
reference  to  infinitation  (supra)  will  apply  a 
fortiori ;  for  here  a  new  term,  "  ZY,"  is  in- 
troduced, differing  from  Y  in  denotation,  in 
connotation,  and  in  verbal  sign. 

1  But  the  converse  is  not  true, — i.  <*.,  from  the  proposition, 
ZY  is  ZX,  we  cannot  infer  that  Y  is  X  ;  as  will  appear  from 
the  following  diagram  : 


THE   SYLLOGISM  8$ 

It  may  therefore  be  concluded,  as  already 
asserted,  that  all  inference  consists  in  sub- 
stituting, for  terms  of  propositions,  other  terms 
of  equivalent  ratiocinative  value. 

§  81.  FORMAL  AND  MATERIAL  SUBSTITU- 
TIONS.— Substitution  of  terms  may  be  either 
formal  or  material.  The  former  includes  all 
cases  where  the  substituted  term  is  the  original 
term  in  a  modified  form, — as,  where  the  ele- 
ments of  a  complex  term  are  arranged  in  a  dif- 
ferent order,  as,  e.g.,  where  YX  is  substituted 
for  XY ;  or,  as  where  the  original  term  is 
qualified  by  some  other  word  or  words  express- 
ing a  formal  relation  existing  between  the  sub- 
stituted term  and  the  original, — as,  e.  g.,  where 
in  the  proposition  "  Y  is  X,"  we  substitute  for 
"  Y  "  "  some  Y, "  or  for  "  X  "  "  not  Not-X  ' ' ; 
or,  as  in  the  example  given  above,  where  we 
substitute  for  "  negro  "  and  "  fellow-creature  " 
the  terms  "  negro  in  suffering  "  and  "  fellow- 
creature  in  suffering."  Material  substitutions 
are  those  where  a  new  term  is  substituted,  as, 
e.g.,  where  we  substitute  for  a  term  a  syno- 
nym, or  species  for  genus,  or  genus  for  species. 

Ill 

OF    MATHEMATICAL    REASONING 

§  82.  MATHEMATICS  THE  TYPE  OF  ALL 
RATIOCINATION. —Hence  it  would  seem  that 


86  LOGIC 

the  most  perfect  type  of  ratiocination  is  pre- 
sented by  the  mathematical,  and  especially  by 
the  algebraic  methods  of  demonstration ;  and 
this  is,  in  fact,  the  case,  as  may  be  illustrated 
by  two  familiar  examples: 

ist  Example.  Thesis. — The  angles  of  a  plain 
triangle  are  together  equal  to  two  right  angles; 
or,  referring  to  the  figure,  a  -f-  b  -j-  c  =  /K 
(Euclid,  Book  I.,  Prop.  XXXII.). 


For 

a  +  b'  +  c'  =  &.    (/£,  Prop.  XXIX.). 

But 

b'  =  b 

c'  =  C. 

Hence,  substituting  equivalents, 

a-|-b'  +  c'  =  a-)-b-(-c=  i\\.     Q.  E.  D. 

zd  Example.  T/iesis. — The  formula  for  com- 
pound interest,  i.  e.,  S  =  p  (1  -f-  r)n,  in  which 
p  =  principal,  n  =  number  of  years,  r  =  rate 
of  interest,  and  S  =  the  amount. 

At  end  of  first  year 

S  =  p  +  pr  =  p  (1  +  r). 
At  end  of  second  year 

S  =  p(l  +  r)+pr(l  +  r)  =  p(l  +  r)-. 


THE   SYLLOGISM  8/ 

At  end  of  third  year 

S  =  p  (1  +  r)'  +  pr  (1  +  r)'  =  p  (1  +  0°. 
At  the  end  of  n  years 

S  =  p  (1  +  r)n. 

§  83.  A  CURRENT  ERROR  ON  THIS  POINT. 
— It  is  indeed  asserted  by  recent  logicians  that 
there  is  an  essential  difference  between  ordinary 
and  mathematical,  or,  as  it  is  otherwise  ex- 
pressed, between  qualitative  and  quantitative 
reasoning.  But  this  opinion  arises  from  the 
failure  to  reflect  that  the  comparison  of  magni- 
tudes can  be  effected  only  by  means  of  units  of 
measurement  that  can  be  applied  equally  to 
the  magnitudes  compared,  and  that  these  con- 
stitute the  significates  denoted  by  mathemati- 
cal terms.  Hence  mathematical  reasoning 
consists  not  in  directly  comparing  the  magni- 
tudes considered,  but  in  comparing  the  units 
that  represent  them ;  and  mathematical  terms 
must  therefore  be  regarded  as  denoting  —  like 
other  terms — collections  or  classes  of  individ- 
uals, /.  e. ,  of  the  units  expressed. 

AN  OPINION  OF  MR.  BAIN. — On  this  point 
we  have  the  following  from  Mr.  Bain:  "  Logi- 
cians are  aware  that  the  form  '  A  equals  B,  B 
equals  C,  therefore  A  equals  C  '  is  not  reducible 
to  the  syllogism.  So  with  relation  to  '  greater 


88  LOGIC 

than'  in  the  argument  a  fortiori ;  yet  to  the 
ordinary  mind  these  inferences  are  as  natural, 
as  forcible,  and  as  prompt  as  the  syllogistic 
inference."  But  the  first  expression  is  a  per- 
fect syllogism  differing  from  the  ordinary  form 
only  in  the  different  interpretation  given  to  the 
copula;  and  this  is  true  also  of  the  argument 
a  fortiori,  if  we  give  it  the  form,  "  A  <  B, 
B  <  C  .  *.  A  <  C."  It  is  strange  this  is  not 
recognized  by  the  author;  or,  rather,  would  be 
strange  were  not  the  error  common.  What 
is  meant,  therefore,  is  that  the  mathematical 
cannot  be  reduced  to  the  ordinary  form  of  the 
syllogism.  But  this  is  not  the  case,  for  mathe- 
matical reasoning  can  readily  be  expressed  in 
the  ordinary  logical  forms,  as,  e.  g.,  the  equa- 
tional  syllogism  in  the  two  syllogisms  follow- 
ing: 

a  is  b  b  is  a 

b  is  c  c  is  b 

.'.  a  is  c  .'.  c  is  a; 

and  the  argument  a  fortiori  in  the  following: 
"  a  is  b,  b  is  c,  .'.  a  is  c,"-— meaning  that  the 
class  of  units  denoted  by  a  is  contained  in  the 
class  denoted  by  b,  etc. 

Or  the  inequalities  may  be  converted  into 
equations,  as,  e .  g. ," a  <  b  "  into  "  a  -f-  x  =  b, " 
and  the  argument  then  be  expressed  in  two 
syllogisms  as  above. 


THE  SYLLOGISM  89 

§  84.  REDUCTION  OF  EUCLID'S  FIFTH 
PROPOSITION  TO  SYLLOGISMS. — Recognizing 
the  mathematical  form  of  the  syllogism,  there 
is  no  need  of  the  cumbersome  method  usually 
adopted  for  the  reduction  of  mathematical 
reasoning  to  syllogistic  form,  as,  e.  g.,  in  the 
ancient  example  of  the  reduction  of  Euclid's 
Fifth  Proposition  given  by  Mansel  in  his  notes 
to  Aldrich  ;  or  the  reduction  of  the  same  prop- 
osition by  Mill  (Logic,  p.  142). 

In  fact,  Euclid's  demonstration  is  itself  in 
syllogistic  form,  and  needs  only  a  slight  varia- 
tion in  the  statement  of  it  to  make  this  ap- 
parent, as,  e.  g.,  as  follows: 

Prop.  V.  The  angles  at  the  base  of  an 
isosceles  triangle  are  equal  to  one  another. 

Or,  referring  to  the  figure,  in  the  isosceles 
triangle  ABC  the  angles  a  and  c  are  equal. 

The  figure  is  constructed  by 
producing  the  equal  sides  A  B 
and  A  C  to  D  and  E,  making 
the  lines  A  D  and  A  E  equal, 
and  by  drawing  the  lines  B  E 
and  D  C. 

Demonstration 

1ST   SYLLOGISM 

Major  Premise.  —  Prop.  IV. 

Minor  Premise.  — The  triangles  ABE  and 


90  LOGIC 

A  C  D  are  triangles  having  two  sides  of  the  one 
equal  to  two  sides  of  the  other,  each  to  each, 
and  the  included  angle  equal. 

Conclusion. — They  are  therefore  equal  in  all 
their  corresponding  parts,  and  hence  B  E  = 
C  D  and  the  angle  d  =  the  angle  e. 


2D   SYLLOGISM 


Major  Premise.  —  Prop.  IV. 

Minor  Premise.  • — The  triangles  C  B  E  and 
BCD  are  triangles  having  two  sides  of  the  one 
equal  to  two  sides  of  the  other,  each  to  each, 
and  the  included  angle  equal. 

Conclusion. — They  are  therefore  equal  in  all 
their  corresponding  parts,  and  hence  the  angle 
f  =  the  angle  g. 

3D   SYLLOGISM 

Major  Premise,  a  —  d  —  f.  (Judgment,  or 
intuitive  proposition.) 

Minor  Premise,  d  —  f  =  e  —  g. 
Conclusion,  a  =  e  —  g. 

4TH   SYLLOGISM 

Major  Premise,  a  =  e  —  g. 
Minor  Premise,  e  —  g  =  c. 
Conclusion,  a  =  c. 


CHAPTER  V 


SUMMARY   OF   THE  TRADITIONAL   LOGIC 


OF    THE    TRADITIONAL    LOGIC    GENERALLY 

§  85.  As  explained  in  the  preface,  one  of 
the  principal  objects  of  this  work  is  to  vindi- 
cate, as  against  modern  innovations,  the  old  or 
traditional  Logic;  and  accordingly,  in  all  that 
has  been  said  —  with  exceptions  to  be  noted 
presently — I  have  kept  close  to  the  traditional 
view,  as  expounded  by  Aristotle  and  the  most 
approved  of  the  older  logicians.  I  have,  in- 
deed, repudiated  the  doctrine  advocated  by 
Whately,  and  by  modern  logicians  generally, 
that  would  distinguish  between  the  formal  and 
the  material  relations  of  terms,  and  restrict  the 
scope  of  Logic  to  the  former;  but  in  this  also 
I  follow  Aristotle  and  the  better  authorities. 

The  only  particulars,  therefore,  in  which  I 
have  departed  from  the  traditional  view  of 
Logic  are:  (i)  that  I  reject  the  "  Particular 
Propositions  "  of  the  old  Logic  and  those  parts 
of  the  old  doctrine  of  the  Proposition  and  of 
91 


92  LOGIC 

the  Syllogism  that  are  founded  on  this  view 
of  the  proposition  ;  and  (2)  that  I  have  adopted, 
in  place  of  the  Dictum,  the  Principle  of  Sub- 
stitution ;  which  is  an  obvious  corollary  from 
the  Dictum,  and  is  more  readily  understood 
and  applied. 

At  the  same  time,  it  must  be  admitted,  the 
old  doctrines  of  the  Proposition  and  the  Syl- 
logism are  remarkable  for  the  accurate  analysis 
upon  which  they  rest,  and  the  wonderful  ingen- 
uity and  acuteness  with  which  they  have  been 
developed.  They  have  thus  become  part  of 
the  accepted  philosophy  of  the  world  ;  and  there 
has  thus  been  developed  a  technical  language 
that  has  come  to  be  universally  received  and  so 
generally  used  that,  without  an  understanding 
of  it,  all  the  literature  on  the  subject  must  be 
a  closed  book  to  us.  I  now  propose,  therefore, 
to  give  a  brief  exposition  of  these  doctrines. 

II 

THE   TRADITIONAL  DOCTRINE   OF   THE    PROPOSITION 

§  86.  QUALTITY  OF  PROPOSITIONS. —  Prop- 
ositions are  said  to  differ  in  quality  accord- 
ingly as  they  are  affirmative  or  negative.  Thus 
the  propositions  "  All  Y  is  X  and  "  Some 
Y  is  X  "  are  affirmative  ;  the  propositions  "  No 
Y  is  X  "  and  "  Some  Y  is  not  X,"  negative. 

§  87.  QUANTITY  OF  PROPOSITIONS. — Again, 
propositions,  whether  affirmative  or  negative, 


TRADITIONAL  LOGIC 


93 


are  said  to  differ  in  quantity  accordingly  as  the 
predicate  is  asserted,  or  denied  universally  of 
all  individuals  of  the  class  denoted  by  the  sub- 
ject or  only  part  of  such  individuals.  In  the 
former  case  the  subject  is  said  to  be  distributed, 
and  the  proposition  is  called  universal ;  in  the 
latter,  the  subject  is  undistributed,  and  the 
proposition  is  said  to  be  particular.  Thus, 
e.  g.,  the  propositions,  "  All  Y  is  X"  and 
4  No  Y  is  X  "  are  both  universal;  and  the 
propositions,  "  Some  Y  is  X  "  and  "  Some  Y 
is  not  X,"  both  particular. 

§  88.  TABLE  OF  PROPOSITIONS. —  Hence, 
four  forms  of  propositions  are  recognized  by  the 
old  logicians,  viz.  :  (i)  the  Universal  Affirma- 
tive ;  (2)  the  Universal  Negative  ;  (3)  the  Par- 
ticular Affirmative;  and  (4)  the  Particular 
Negative ;  which  are  designated  respectively 
by  the  letters  A,  E,  I,  and  O;  and,  with  their 
expressions  in  Euler's  Symbols,  are  as  fol- 
lows, viz. : 

A:     Y  is  X  (/.<?.,  All  Y  is  X) 

E:     Y  is  not  X  (/.  e.,  No  Y  is  X) '    (Y) 
I:      Some  Y  is  X 


O:     Some  Y  is  not  X 
1  The  above  differs  somewhat  from  the  ordinary  notation  ; 


94  LOGIC 

In  the  negative  propositions,  E  and  O,  it 
will  be  observed,  the  predicate  is  distributed  or 
taken  universally ;  in  the  affirmative  proposi- 
tions it  is  undistributed. 

§  89.  OPPOSITION  OF  PROPOSITIONS. — Two 
propositions  are  said  to  be  opposed  to  each 
other  when,  having  the  same  subject  and  pred- 
icate, they  differ  in  quantity  or  quality,  or  both. 

Propositions  that  differ  both  in  quality  and 
quantity,  as  A  and  O,  or  E  and  I,  are  called 
contradictories,  as,  e.  g. ,  "  Y  is  X,"  and  "  Some 
Y  is  not  X  "  ;  or  "  Y  is  not  X  "  and  "  Some 
Y  is  X."  Those  that  differ  in  quality  only,  if 

according  to  which  it  is  thought  necessary  in  A  and  E  to  use 
the  signs  "  All "  and  "  No,"  in  order  to  indicate  that  the  sub- 
ject is  distributed,  as,  e.  g.,  "All  Y  is  X,"  "No  Y  is  X." 
But,  properly  speaking,  the  signs  "All"  and  "  No"  are  un- 
necessary and  redundant.  For  when  we  say,  e.  g.,  "Man  is 
mortal,"  or  "  Man  is  not  mortal"  we  mean,  when  we  speak 
properly,  that  in  the  former  case  the  class  "man"  is  wholly 
included  in,  and  in  the  latter  that  it  is  wholly  excluded  from, 
the  class  "  mortal "  ;  or,  in  other  words,  as  the  case  may  be, 
that  "  All  men  are  mortal"  or  that  "  No  man  is  mortal" 
(§  53.  n-)-  The  last  expression  is  also  objectionable  on  ac- 
count of  the  liability  to  confound  the  expression  "  No  man  " 
with  the  term  "  Not-man  "  in  converting  either  of  the  above 
propositions  by  contraposition  (for  which  see  infra,  §  91)  ; 
or  (more  generally)  the  negative  proposition  "No  Y  is  X  " 
is  liable  to  be  confounded  with  the  affirmative  proposition, 
"ATot-  Y  is  X."  Hence  it  will  be  preferable  to  regard  the 
subject  as  always  distributed,  except  where  it  is  preceded  by 
the  adjective  "  some  "  ;  and,  in  place  of  the  sign  "  no"  before 
the  subject,  to  use  the  particle  "  not "  after  the  copula. 


TRADITIONAL   LOGIC  95 

universal,  are  called  contraries,  as,  e.  g.,  "  Y  is 
X  "  and  "  Y  is  not  X  "  ;  and  if  particular,  sub- 
contraries,  as,  e.  g.,  "  Some  Y  is  X  "  and 
"  Some  Y  is  not  X."  Where  propositions 
differ  in  quantity  only,  as  A  and  I,  or  E  and 
O,  the  particular  propositions  are  called  subal- 
terns, as,  e.  g. ,  "  Y  is  X  "  and  "  Some  Y  is 
X  ";  and  "  Y  is  not  X  "  and  "  Some  Y  is 
not  X." 

There  are,  therefore,  four  kinds  of  opposition 
recognized  by  logicians,  viz.  :  (i)  the  opposi- 
tion of  contradictories  ;  (2)  that  of  contraries  ; 
(3)  that  of  subcontraries,  and  (4)  that  of  subal- 
terns to  their  corresponding  universals;  which, 
with  their  relations  to  each  other,  are  admi- 
rably expressed  in  the  following  table,  which 
has  come  to  us  from  ancient  times: 


!\  /\ 
I  V  I 

5  <*        "**> 

V    \\ 


-SUBCOMTRARY- 


(i)  CONTRADICTORIES.  The  most  complete 
kind  of  opposition  is  that  of  contradictories. 
These  cannot  both  be  either  true  or  false:  i.  e., 
if  one  is  true,  the  other  is  false;  or,  if  one  is 


96  LOGIC 

false,  the  other  is  true.  For  if  it  be  true  that 
"  All  men  are  sinners,"  it  cannot  be  true  that 
"  Some  men  are  not  sinners  "  ;  and,  conversely, 
if  it  be  true  that  "  Some  are  not  righteous,"  it 
cannot  be  true  that  "  All  men  are  righteous." 
In  other  words,  between  contradictories  there 
is  no  intermediate  proposition  conceivable ;  one 
must  be  true  and  the  other  false.  This  is 
called  the  law  of  Excluded  Middle. 

(2)  CONTRARIES.      Contraries  cannot  both 
be  true;  for  if  it  be  true  that  "  Every  man  is 
an  animal,"  it  must  be  false  that  "  No  man  is 
an  animal."     But  both  may  be  false,  as,  for 
example,  the  propositions  that  "  All  men  are 
learned,"  and  that  "  No  men  are  learned"; 
which  are  both  false,  for  some  are  learned  and 
some  are  not.     In  other  words,  contrary  propo- 
sitions do  not  exclude  the  truth  of  either  of  the 
particular  propositions  between  the  same  terms. 

(3)  SUBCONTRARIES.     Subcontraries  are  con- 
trasted  with  contraries  by  the  principle  that 
they  may  be  both   true,  but  cannot  both  be 
false.     Thus  it  may  be  true  that  "  Some  men 
are  just,"  and  also  that  "  Some  men  are  not 
just  "  ;  but  if  it  be  false  that  "  Some  men  are 
just,"  it  must  be  true  that  "  No  man  is  just," 
— which  is  the  contradictory, — and,  a  fortiori, 
that  "Some  men  are  not  just," — which  is  the 
subcontrary. 

(4)  SUBALTERNATE  OPPOSITION.      With  re- 


TRADITIONAL  LOGIC  97 

gard  to  subaltern  propositions,  their  truth 
follows  from  the  corresponding  universal  pro- 
positions; for  if  "  all  men  are  animals,"  "  some 
men  are  animals,"  and  if  "  no  man  is  an  ape," 
"  some  men  are  not  apes."  But  from  the  truth 
of  a  subaltern  proposition  we  cannot  infer  the 
truth  of  the  corresponding  universal,  as,  e.  g., 
from  the  proposition  "  Some  men  are  false," 
the  proposition  "  All  men  are  false  ";  or  from 
the  proposition  "  Some  men  are  not  false,"  the 
proposition  that  "  No  man  is  false." 

§  90.  OBSERVATIONS  UPON  CONTRARY  AND 
CONTRADICTORY  OPPOSITIONS. —  Accurately 
speaking,  these  constitute  the  only  kinds  of 
opposition.  Subcontraries  are,  in  fact,  not  op- 
posites;  and  the  same  is  true  of  subalterns  and 
their  corresponding  universals. 

It  will  be  observed  it  does  not  follow  from 
the  principle  of  contrary  opposition  that  of 
two  terms  regarded  as  subject  and  predicate — 
as,  e.  g. ,  Y  and  X — either  the  latter  or  its 
negative  may  always  be  predicated  of  the 
former,  or,  in  other  words,  that  Y  must  be 
either  X,  or  not  X;  for,  in  fact,  some  Y  may 
be  X,  and  some  Y  not  X,  as  will  obviously 
appear  from  the  following  diagrams: 


©0 


98  LOGIC 

Hence  there  arises,  seemingly,  a  puzzling 
contradiction  between  this  principle  and  the 
law  of  Excluded  Middle — as  it  is  often  stated. 
Thus,  it  is  said,  "  Rock  must  be  either  hard  or 
not  hard"  (Jevons,  Lessons  in  Logic,  p.  119), 
or,  generally,  "  Y  is  either  X  or  not  X."  But 
obviously  this,  unless  accidentally,  is  not  true; 
for  some  rock  may  be  hard  and  some  soft ;  or 
some  Y  may  be  X,  and  some  not  X.  And  so 
we  cannot  say  of  "  men  "  either  that  they  are 
learned  or  that  they  are  not  learned ;  for  some 
are  the  one  and  some  the  other.  But  the  ap- 
parent contradiction  arises  from  the  misstate- 
ment  of  the  law  of  Excluded  Middle;  which 
is  itself  nothing  more  or  less  than  the  principle 
governing  contradictories,  as  expressed  above. 
We  may,  indeed,  where  a  subject  term  (as, 
e.  g.,  Y)  denotes  an  individual  or  single  thing 
(real  or  fictitious),  affirm  of  it  that  it  is  either 
X  or  not  X;  but  if  Y  denotes  a  class  of  more 
than  one  we  cannot  so  affirm.1 

1  Even  Hobbes  falls  into  the  error  of  Jevons  on  this  point. 
"Positive  and  negative  terms,"  he  says,  "are  contradictory 
to  one  another,  so  that  they  cannot  both  be  the  name  of  the 
same  thing.  Besides,  of  contradictory  names,  one  is  the  name 
of  anything  whatsoever  (i.  e.,  of  any  conceivable  thing),  for 
whatsoever  is,  is  either  a  man,  or  not  a  man,  white,  or  not 
white,  and  so  of  the  rest."  But,  it  may  be  asked,  "  Does  the 
name  'biped'  denote  (universally)  either  man,  or  not  man?"  or 
"  the  name  'man',  either  white  man,  or  man  not  white?" 

The  confusion  results  from  the  technical  view  that  regards 


TRADITIONAL   LOGIC  99 

§  91.  CONVERSION  OF  PROPOSITIONS. — A 
proposition  is  said  to  be  converted  when  its 
terms  are  transposed,  i.  e.,  when  the  subject  is 
made  the  predicate  and  the  predicate  the  sub- 
ject (§  54).  Such  conversion  is  admissible 
only  when  illative,  i.  e.,  where  the  truth  of  the 
converse  is  implied  in  that  of  the  original  prop- 
osition. When  such  conversion  can  be  made 
without  otherwise  changing  the  proposition  it 
is  called  a  simple  conversion;  otherwise,  it  is 
called  a  con  version  per  accidens.  Thus  A  ("  Y 
is  X  ")  cannot  be  converted  simply,  because  the 
subject  only  is  distributed;  we  therefore  can- 
not say  that  "  All  X  is  Y,"  but  only  that 
"  Some  X  is  Y,"  which  is  called  conversion  per 
accidens.  But  E  ("  Y  is  not  X  ") — as  both  sub- 
ject and  predicate  are  distributed — may  be  con- 
verted simply ;  or,  in  other  words,  we  may  say 

the  Particular  Proposition  as  a  form  distinct  from  the  Uni- 
•versal,  and  its  source  would  be  removed  if,  as  elsewhere 
suggested,  this  form  of  the  proposition  should  be  rejected 
(§  52,  n.).  We  might  then  adopt,  as  equally  accurate 
and  profound,  the  remaining  observation  of  Hobbes,  that 
"the  certainty  of  this  axiom,  namely,  that  of  two  contradic- 
tory names  one  is  the  name  of  anything  whatsoever,  the  other 
not,  is  the  original  and  foundation  of  all  ratiocination,  that 
is,  of  all  philosophy"  (Logic,  Sec.  8),  which  is  in  accord  with 
the  view  of  Aristotle  :  "  For  the  same  thing  to  be  present  and 
not  to  be  present,  at  the  same  time,  in  the  same  subject,  and 
in  the  same  sense,  is  impossible.  .  .  .  For  by  nature  this 
is  the  first  principle  of  all  the  other  axioms "  (Metaphysics, 
R.  iii.,  chap.  Hi.). 


IOO  LOGIC 

that  "  No  X  is  Y."  So  with  I  ("  Some  Y  is 
X  "), — as  both  subject  and  predicate  are  un- 
distributed,—  the  proposition  may  be  simply 
converted,  i.  e.,  if  "  Some  Y  is  X,"  then  it  is 
necessarily  true  that  "  Some  X  is  Y." 

By  one  or  the  other  of  these  methods,  i.  e., 
either  simply  or  per  accidens,  all  propositions  of 
the  forms  A,  E,  and  I  may  be  converted.  But  O 
("  Some  Y  is  not  X  ")  cannot  be  thus  converted. 
Thus,  e.  g.,  it  cannot  be  inferred  from  the  prop- 
osition "Some  Greeks  are  not  Athenians" 
that  "  Some  Athenians  are  not  Greeks."  But 
such  conversion  may  be  effected  by  simply  re- 
garding the  negative  particle  (not)  as  part  of 
the  predicate  ;  by  which  expedient  O  is  changed 
into  I,  and  may  be  simply  converted,  as,  e.  g., 
"Some  Greeks  are  Not-Athenians  "  ;  which 
may  be  converted  into  the  proposition  "  Some 
Not-Athenians  are  Greeks. ' '  So  from  the  prop- 
osition "  Some  men  are  not  learned,"  though 
we  may  not  infer  that  "  Some  learned  are  not 
men,"  we  may  infer  that  "  Some  unlearned 
are  men."  This  is  called  by  the  old  logi- 
cians "Conversion  by  Contraposition,"  and  by 
Whately,  "  Conversion  by  Negation." 

This  method  of  conversion  is  applicable  to 
A  and  E  as  well  as  O,  and,  as  it  is  of  very  ex- 
tensive use,  we  append  a  table  of  such  conver- 
sions, taken,  with  some  alterations,  from  De 
Morgan  (Formal  Logic,  p.  67).  In  this  table 


TRADITIONAL   LOGIC  IOI 

(altering  De  Morgan's  notation)  the  original 
terms  of  the  proposition  are  denoted  by  the 
capital  letters  Y  and  X,  and  their  contraries 
respectively  by  prefixing  the  Greek  privative  a. 
We  append  also  for  illustration  the  symbolical 
expressions  for  the  several  propositions: 

A:  "  Y  is  X  "  ;  "  Y  is  not  aX  "  ;  "  aX  is  not  Y  "  ; 
"  aX  is  aY  "  : 


The  righteous  are  happy 
The  righteous  are  not  unhappy  / 
The  unhappy  are  not  righteous  ' 
The  unhappy  are  unrighteous. 


E:  "YisnotX";  "  Y  is  aX  "  ;  "  Some  aX  is  Y  "  ; 

"  Some  aX  is  not  aY." 

"  X  is  not  Y  "  ;    "  X  is  aY  "  ;    "  Some  aY  is  X  "  ; 
"  Some  aY  is  not  aX  "  : 

Perfect  virtue  is  not  human  ''    \j       \ 

Perfect  virtue  is  unhuman  IS~\      «/f~\\ 

Y  Ca  A  I     X    I 


Some  unhuman  virtue  is  perfect  v^ 

Some  unhuman  virtue  is  imperfect.        \  , 

^^ *s 

Human  virtue  is  not  perfect 
Human  virtue  is  imperfect 
Some  imperfect  virtue  is  human 
Some  imperfect  virtue  is  not  unhuman. 

O:  "  Some  Y  is  not  X  "  ;  "  Some  Y  is  aX  "  ;  "  Some 
aX  is  Y  "  ;  "  Some  aX  is  not  aY  "  : 


102  LOGIC 

Some  possible  cases  are.  not  probable 

Some  possible  cases  are  not  improb- 
able 

Some  improbable  cases  are  possible 

Some  improbable  cases  are  not  im- 
possible. 

It  will  be  observed  from  the  above  table  that 
a  universal  affirmative  proposition  can  always 
be  converted  into  another  universal  affirmative 
between  the  contradictories  of  its  original  terms 
by  simply  reversing  the  order  of  the  terms  and 
substituting  for  them  their  contradictories. 

§  92.  OF  MATERIAL  CONVERSIONS. — It  will 
be  observed  that  the  conversions  of  propositions 
treated  by  logicians  have  regard  to  the  dis- 
tinction, heretofore  explained,  between  the 
formal  and  the  material  relations  of  terms 
(§  66  (2)),  and  are  confined  exclusively  to  what 
may  be  called  formal  conversions,  i.  e.,  to  cases 
where  the  equivalence  of  the  converted  and 
original  propositions  results  from  the  formal  or 
general  relations  of  terms.  But  conversions  of 
propositions  based  upon  the  material  relations 
of  terms  are  of  essentially  the  same  nature,  as, 
e.  g.,  where  the  proposition  "  John  is  the  son 
of  William  "  is  converted  into  the  proposition 

William  is  the  father  of  John";  or  the 
proposition"  Cain  murdered  Abel"  into  the 
proposition  "  Abel  was  murdered  by  Cain,"  or 
into  the  proposition  "  Cain  is  the  man  that 


TRADITIONAL   LOGIC  103 

murdered  Abel."  These,  having  regard  to 
the  received  distinction  between  the  formal 
and  the  material  relations  of  terms,  may  be 
called  material  conversions ;  and  are  infinitely 
the  more  numerous  class,  and  equally  deserv- 
ing of  attention.  But  though  conversions  of 
this  kind  are  in  constant  use,  and  though,  in- 
deed, we  cannot  proceed  a  step  in  our  logical 
processes  without  them,  yet  the  subject  has 
received  but  little  attention,  and  remains  as 
yet  a  vast,  unexplored  domain.1  It  can  only 
be  said,  therefore,  in  the  present  condition  of 
logical  doctrine,  that  as  the  distinction  be- 
tween the  formal  and  the  material  relations  of 
terms  has  been  found  unessential,  so  must  the 
distinction  between  formal  and  material  con- 
versions be  regarded.  Both  classes  of  conver- 

1  To  this  domain  belong  such  subjects  as  the  "Categories" 
"Intensive  Propositions,''''  "  Hypothetical  Propositions"  and, 
in  short,  all  forms  of  expression  that  differ  from  the  ordinary 
logical  proposition.  With  these  Logic  is  concerned  only  in 
so  far  as  is  involved  in  their  conversion  into  logical  forms. 
Otherwise,  neither  the  Intensive  nor  the  Hypothetical  Logic 
(if  we  may  give  either  the  name)  can  be  regarded  as  part  of 
Logic  as  traditionally  received  ;  which  is  based  exclusively 
upon  the  logical  form  of  the  proposition  and  its  extensive 
interpretation.  With  regard  to  the  Hypothetical  Logic,  it 
will  be  observed,  it  has  no  place  in  Aristotle's  treatises  ;  and 
Mansel  is  of  the  opinion — in  which  I  agree — that  in  this  he 
showed  a  juster  notion  of  the  scope  of  Logic  than  his  suc- 
cessors. The  subject  is  well  treated  in  the  current  works  on 
Logic,  and  is  worthy  of  some  attention  from  the  student. 


104  LOGIC 

sions  rest  equally  for  their  validity  simply 
upon  judgments  as  to  the  equivalence  of  ex- 
pressions. 

Ill 

THE    TRADITIONAL    DOCTRINE    OF     THE     SYLLOGISM 

§  93.  The  following  epitome  of  the  doctrine 
of  the  syllogism  as  traditionally  received,  brief 
as  it  is,  will — with  what  has  already  been  said 
—  be  found  amply  sufficient  to  expound  it. 
It  will,  indeed,  require  the  same  close  attention 
and  thought  as  is  usually  given  to  mathemati- 
cal demonstrations;  but  it  may  be  said  that 
to  those  who  are  unwilling  to  give,  or  are  in- 
capable of  giving,  to  it  this  kind  of  thought, 
the  study  of  Logic  cannot  be  of  much  benefit. 

I .    Of  the  Moods  and  Figures  of  the  Syllogism 

§  94.  MOODS  OF  THE  SYLLOGISM.— The  syl- 
logism is  said  to  be  in  different  moods,  according 
to  the  occurrence  and  arrangement  in  it  of  the 
several  forms  of  the  proposition— A,  E,  I,  and 
O;  as,  e.  g.,  in  the  syllogism  Y  is  X,  Z  is 
Y,  .  *.  Z  is  X, ' '  which  consists  of  three  universal 
affirmative  propositions,  and  is,  therefore,  said 
to  be  in  the  mood  A  A  A. 

The  four  forms  of  the  proposition,  A,  E,  I, 
O,  may  be  arranged,  in  sets  of  three  each,  in 
sixty-four  different  ways,  but  upon  examina- 
tion it  is  found  that  of  these  there  are  eleven 


TRADITIONAL   LOGIC  1 05 

arrangements  only  that  constitute  valid  syllo- 
gisms; and  hence  the  legitimate  syllogism  can 
have  but  eleven  moods,  viz.  : 

Table  of  Moods 

A  A  A,  A  A  I,  A  E  E,  A  E  O,  A  I  I, 
A  O  O,  E  A  E,  E  A  O,  E  I  O,  I  A  I,  O  A  O. 

§  95.  FIGURES  OF  THE  SYLLOGISM. — Again, 
syllogisms  are  said  to  be  of  different  figures, 
according  to  the  position  of  the  middle  term  in 
the  syllogism  with  reference  to  the  extremes; 
and  as  there  are  said  to  be  four  different  ways 
in  which  the  middle  term  may  be  thus  placed, 
syllogisms  are  said  to  have  four  figures,  viz.  : 
the  1st  figure,  where  the  middle  term  is  the 
subject  of  the  major  and  the  predicate  of  the 
minor  premise  ;  the  2d,  where  it  is  fa& predicate 
both  of  the  major  and  of  the  minor  premise ; 
the  3d,  where  it  is  the  subject  of  both  the  major 
and  the  minor  premise ;  and  the  4th,  where  it 
is  the  predicate  of  the  major  and  the  subject  of 
the  minor  premise.  Thus — using  the  conven- 
tional symbols  —  the  forms  of  the  different 
figures  are  usually  expressed  as  follows : 

Table  of  Figures 

1st  Fig.  2cl  Fig.  3d  Fig.  4th  Fig. 

Y    X,  X   Y,  Y    X,  X   Y, 

Z    Y,  Z    Y,  Y    Z,  Y    Z, 

Z    X,  Z    X,  Z    X,  Z    X. 


106  LOGIC 

If  the  eleven  moods  of  the  syllogism  were  all 
valid  in  each  of  the  four  figures,  there  would 
result  forty-four  different  kinds  of  syllogisms 
differing  in  mood  or  figure.  But  none  of  the 
moods  are  valid  in  all  the  figures;  and  it  is 
found  on  examination  that  there  are  in  fact 
only  twenty-four  kinds  of  syllogisms  that  are 
valid ;  and  that  of  these  five  are  useless.  So 
that  the  number  of  different  kinds  of  legiti- 
mate syllogisms  recognized  by  logicians  is 
nineteen. 

§96.  REDUCTION  OF  SYLLOGISMS. —  All 
these  forms  may,  however,  be  reduced  or  con- 
verted—  without  affecting  their  validity — into 
the  form  of  the  first  figure ;  which  is  accord- 
ingly regarded  by  logicians  as  the  principal,  or 
normal  figure  of  the  syllogism.  The  different 
figures  and  moods  of  the  syllogism,  and  the 
methods  of  reduction  or  conversion  from  one 
figure  to  another,  are  briefly  expressed  in  the 
following  hexameter  verses,  constituting  what 
may  be  called 

The  Table  of  Syllogisms 

Fig.  i — Barbara,  Olar^nt,  Dam,  Ferioque,  prioris 
Fig.  2 — Cesare,  Canvstr^s,  Festino,  Fak^n?,  secundae 
Fig.  3 — Tertia,  Darapti,  D/sam/s,  Dat/sz',  Fi?lapt<?n, 

D0kam0,  Feriso,   habet,  quarta  insuper 

addit 
Fig.    4 — Bramant/p,    Camenes,     D/man's,     Fesapo, 

Fresison. 


TRADITIONAL   LOGIC  IO/ 

In  these  lines  the  words  commencing  with 
capital  letters  (except  "  Tertia  ")  are  the  names 
of  the  several  syllogisms  in  each  figure,  and 
the  italicized  vowels  point  out  the  moods  of 
the  propositions  constituting  the  several  syl- 
logisms. Thus,  e.  g.,  the  vowels  indicate  that 
Barbara  consists  of  the  three  propositions,  A, 
A,  A;  Celarent  of  E,  A,  E;  Darn  of  A,  I,  I ; 
Feriso  of  E,  I,  O,  etc. 

The  initial  letter  in  the  name  of  each  syllo- 
gism in  the  second,  third,  and  fourth,  or,  as 
they  are  called,  the  indirect  figures,  indicates 
that  the  given  syllogism  is  to  be  reduced  to  the 
syllogism  in  the  first  figure  commencing  with 
the  same  letter,  as,  e.  g,,  Cesare,  Camestres, 
Camenes  into  Celarent ;  Bramantip  into  Bar- 
bara ;  Daraptiy  etc.,  and  Dimaris,  etc.,  into 
Darii ;  Festino,  etc.,  Felapton,  etc.,  and  Fesapo, 
etc.,  into  Ferio. 

The  letters  s,  p,  and  k  indicate  that  the  pro- 
position indicated  by  the  vowel  immediately 
preceding  is  to  be  converted  —  s  indicating 
simple  conversion,  /  conversion  per  accidens, 
and  k  conversion  by  contraposition,  or  nega- 
tion. ' 

1  The  use  of  conversion  by  contraposition  as  a  means  of 
reduction  is  a  late  invention.  It  is,  in  general,  used  only  in 
the  two  forms,  Fakoro  and  Dokamo, — or,  as  they  were  origi- 
nally called,  Baroko  and  Bokardo, — as  all  other  forms  can  be 
reduced  without  its  aid,  i.  e.,  by  the  use  of  simple  conversion 
or  conversion  per  accidens.  Prior  to  the  use  of  this  method, 


io8  LOGIC 

The  letter  m  indicates  that  the  premises  are 
to  be  transposed. 

The  other  letters  are  without  significance. 

TABLE  OF  SYLLOGISMS.  By  the  use  of  the 
'  Table  of  Moods"  and  the  "  Table  of  Fig- 
ures," all  the  syllogisms  given  in  the  "  Table 
of  Syllogisms"  may  be  readily  constructed, 
and  the  mode  of  reducing  the  syllogisms  in  the 
second  and  third  and  fourth  figures  to  the  cor- 
responding syllogisms  in  the  first  figure  be 
readily  perceived.1 

Baroko  and  Bokardo  could  not  be  directly  reduced  to  the  first 
figure,  but  indirectly  only  by  a  process  called  rednctio  ad 
impossible ;  which  consisted  in  substituting  for  one  of  the 
premises  the  contradictory  of  the  conclusion. 

By  this  method  Baroko  is  converted  into  a  syllogism  in  Bar- 
bara, having  the  contradictory  of  the  original  conclusion  for  a 
minor  premise,  and  the  contradictory  of  the  original  minor 
premise  for  a  conclusion,  which,  as  the  minor  premise  is  true 
ex  hypothese,  is  an  absurdity,  viz.  : 

(Original  Syllogism)  (Reduced  Syllogism) 

X  is        Y  X  is  Y 

Some  Z  is  not  Y  Z  is  X 

.'.  Some  Z  is  not  X  .'.  Z  is  Y 

By  the  same  method  Bokardo  is  converted  into  a  syllogism 
in  Barbara,  having  the  contradictory  of  the  original  conclusion 
for  a  major  premise,  and  the  contradictory  of  the  original 
major  for  a  conclusion,  e.  g.  : 

Some  Y  is  not  X  Z  is  X 

Y  is        Z  Y  is  Z 

. ' .   Some  Z  is  not  X  . ' .  Y  is  X 

1  A  table  of  the  several  syllogisms,  with  their  reductions, 
illustrated  by  Euler's  symbols,  is  appended  (see  Appendix  M). 


TRADITIONAL  LOGIC  109 

§  97.  OBSERVATIONS  UPON  THE  FORMS  OF 
SYLLOGISMS. — It  will  be  observed  from  what 
has  been  said  that  the  numerous  forms  of  syl- 
logisms recognized  by  the  old  logicians  result 
from  two  assumptions — the  one  erroneous  and 
the  other  unnecessary. 

The  first  is  the  erroneous  assumption  that 
the  symbols  Y  and  X  must  always  be  taken  as 
denoting  respectively  the  minor  and  the  major 
terms;  from  which  results  that  there  areyWr 
figures  of  the  syllogism,  instead  of  three.  But 
if  in  the  fourth  figure  we  regard  X  as  the  minor 
term  and  Y  as  the  major,  it  becomes  of  the 
first  figure.  Hence  the  fourth  figure  —  which 
was  not  recognized  by  Aristotle,  but  is  a  late 
invention  —  is  rightly  rejected  by  the  best 
authorities. 

The  other  assumption  is  that  the  particular 
propositions  ("  Some  Y  is  X  "  or  "  Some  Y  is 
not  X  ")  are  to  be  regarded  as  involving  the 
same  terms  as  the  universal  ("  Y  is  X  "  or  "  Y 
is  not  X  "),  and  the  expression  "  some  "  as  a 
mere  sign  of  quantity;  from  which  (and  the 
first  assumption)  there  result  the  four  forms  of 
the  proposition,  A,  E,  I,  and  O,  and  the  nine- 
teen forms  of  syllogism  recognized  by  logicians, 
Barbara,  Celarent,  etc.1 

1  The  doctrine  of  the  syllogism,  and  especially  that  of  its 
moods  and  figures,  has  been  elaborated  by  the  logicians  per- 
haps to  an  unnecessary  extent,  but  as  it  stands  must  always 


I IO  LOGIC 

§  98.  PROPOSED  SIMPLIFICATION  OF 
FORMS. — But  if  in  the  particular  propositions 
(I  and  O)  we  regard  the  expression  "  some  " 
not  as  a  sign  of  quantity,  but  as  part  of  the 
term, — or,  in  other  words,  if  we  regard  "  Some 
Y  "  instead  of  "  Y  "  as  the  term, — they  be- 
come the  same  as"  A"  and  "  E,"  i.  e.,  Univer- 
sal (§  52,  n.).  By  this  simple  change  the  four 
forms  of  the  proposition  are  reduced  to  two  (A 
and  E),  and  the  nineteen  forms  of  syllogism  to 
the  two  simple  forms  of  Barbara  and  Celarent.1 

2.   Of  the  Dictum  de  Omni  et  Nullo 

§  99.  OF  THE  SEVERAL  FORMS  OF  THE 
DICTUM. — The  principle  of  the  syllogism,  or 
the  Dictum  de  Omni  et  Nullo,  has  already  been 
considered  at  length,  and  what  has  been  said  is 
sufficient  to  elucidate  its  nature.  It  is,  how- 
ever, variously  stated  by  logicians,  as  indeed 
by  Aristotle  himself,  and  it  will  be  of  interest 
to  consider  some  of  its  various  forms. 

constitute  a  necessary  part  of  a  liberal  education.  For  prac- 
tical use,  however,  it  is  unnecessarily  complicated  ;  and  it  will 
be  found  that  when  modified,  as  we  have  suggested  (i.  e.,  by 
rejecting  the  particular  proposition,  and  substituting  for  the 
ordinary  form  of  the  dictum  the  Principle  of  Substitution), 
the  simplicity  of  its  application  will  be  largely  increased. 

1  More  accurately,  perhaps,  it  should  be  said  to  four  forms, 
namely,  Barbara,  Celarent,  Cesare,  and  Camestres.  But  the 
last  two  are  essentially  the  same  as  the  second,  and  there  is  no 
advantage  to  be  gained  by  distinguishing  them. 


TRADITIONAL  LOGIC  III 

Of  these,  in  addition  to  the  form  already 
given,  and  which  is  on  all  accounts  to  be  pre- 
ferred, there  are  two  others  to  which  we  will 
refer. 

These,  as  given  by  Whately,  are  as  follows : 
Whatever  is  predicated  \i.  e.,  affirmed  or 
denied]  universally  of  any  class  of  things,  may 
be  predicated  in  like  manner  [viz.,  affirmed  or 
denied]  of  anything  comprehended  in  that 
class  "  (Logic,  bk.  i.,  §  iv.). 

'  Whatever  is  predicated  of  a  term  dis- 
tributed, whether  affirmatively  or  negatively, 
may  be  predicated  in  like  manner  of  everything 
contained  under  it  "(Id.,  bk.  ii.,  chap,  iii.,  §2). 

In  effect,  these  two  statements  may  be  taken 
as  types  of  all  the  other  forms  of  the  dictum. 
But,  as  we  have  observed,  ' '  thing  "  or  "  things 
is  an  extremely  vague  and  unsatisfactory  term, 
and  it  would  be  better  to  substitute  for  it  the 
expression  "  significate,"  or  "  significates." 

These  two  forms  of  the  dictum  are  in  ef- 
fect the  same.  For  to  say,  as  in  the  latter, 
"Whatever  is  predicated  of  a  term  distributed," 
is  in  effect  to  say,  "  Whatever  is  predicated 
universally  of  any  class,"  etc.  Bearing  this 
in  mind,  and  substituting  "  significates  "  for 
"  t Jungs,"  both  forms  of  the  dictum  may  be 
more  briefly  expressed  by  saying  that  "  a  term 
predicated  of  a  term  may  be  predicated  also  of 
any  or  all  of  its  significates."  Where  the  pred- 


112  LOGIC 

ication  is  affirmative  the  principle,  as  we  have 
seen,  is  called  the  Dictum  de  Omni ;  where  it 
is  negative,  the  Dictum  de  Nullo. 

It  is  said  by  Whately  that  the  dictum  "  can- 
not be  directly  or  immediately  applied  to  all 
even  categorical  syllogisms,  but,  as  all  syllo- 
gisms may  be  reduced  to  the  first  figure,  it  may 
be  ultimately  applied  to  all."  Hence,  "  to 
avoid  the  tediousness  of  reducing  all  syllogisms 
to  that  form  to  which  Aristotle's  dictum  is  ap- 
plicable, it  has  been  deemed  necessary  to  in- 
vent separate  rules  or  canons  for  the  indirect 
figures"  (Whately,  Logic,  bk.  ii.,  chap,  iii.,  §  2); 
and  in  this  logicians  generally  agree. 

§  100.  CANONS  OF  THE  SEVERAL  FIGURES. 

—These  canons  of  the  several  figures — omitting 

the  fourth  figure,  which  is  disallowed  by  the 

best  authorities  as  being  a  mere  perversion  of 

the  first — are  as  follows  : 

First  Figure  :  The  Dictum  de  Omni  et  Nnllo, 
as  above. 

Second  Figure:  Dictum  de  Diverse.  If  one 
term  is  contained  in  and  another  excluded  from 
a  third  term,  they  are  mutually  excluded. 

Third  Figure:  Dictum  de  Exemplo.  Two 
terms  which  contain  a  common  part,  partly 
agree,  or,  if  the  one  term  contain  a  part  which 
the  other  does  not,  they  partially  differ  (Devey's 
Logic,  pp.  109-111). 

§  101.  THE  DICTUM,  RIGHTLY  EXPRESSED, 


TRADITIONAL   LOGIC  113 

APPLICABLE  TO  ALL  THE  FIGURES.— But  if 
the  form  of  the  dictum  we  have  adopted,  and 
which  is  substantially  as  given  by  Aristotle 
(§  76),  be  taken,  it  will  be  found  to  apply  to 
all  syllogisms  universally.  But  as  the  form 
given  in  the  paragraph  cited  has  reference  to 
the  division  of  propositions  there  adopted  into 
two  kinds  only  (namely,  A  and  E,  rejecting  I 
and  O),  it  must  now  be  stated  somewhat  differ- 
ently, so  as  to  apply  to  the  ordinary  division 
of  propositions  into  their  four  kinds,  A,  E,  I, 
and  O: 

'  Where  three  terms  (which  we  will  call  the 
middle  and  two  extremes)  so  subsist  with  rela- 
tion to  each  other  that  the  one  extreme  is  in- 
cluded (wholly  or  partly]  in  the  middle,  and 
the  middle  is  included  in  or  excluded  from  the 
other,  then  (as  the  case  may  be)  the  extreme 
included  in  the  middle  will  be  (ivliolly  or  partly) 
included  in  or  excluded  from  the  other  ex- 
treme." 

Or  dividing  the  proposition,  and  leaving  the 
terms  "  wholly  "  or  "partly  "  to  be  supplied 
as  required,  it  may  be  stated  thus: 

Dictum  de  Omni:  (a)  If  one  extreme  of  a 
syllogism  be  included  in  the  middle  and  the 
middle  in  the  other  extreme,  then  will  the 
former  be  included  in  the  latter. 

Dictum  de  Nullo :  (b)  If  one  extreme  of  a 
syllogism  be  included  in  the  middle,  and  the 


1 14  LOGIC 

middle  be  excluded  from  the  other,  then  will  the 
former  extreme  be  excluded  from  the  latter. 

In  this  form  the  dictum  may  be  readily  ap- 
plied to  each  of  the  three  figures. 

With  regard  to  the  first  this  is  sufficiently 
obvious;  for  the  syllogisms  in  this  figure  are 
in  fact  but  mere  symbolical  expressions  of  the 
dictum  — that  is  to  say,  Barbara  and  Darii  of 
the  Dictum  de  Omni,  and  Celarent  and  Fcrio 
of  the  Dictum  de  Nullo. 

With  regard  to  the  second  figure,  the  Dictum 
de  Nullo  is,  in  effect,  identical  with  the  Dictum 
de  Diverso.  For  to  say,  as  is  said  in  the  former, 
that  "  the  middle  term  is  excluded  from  the 
last  extreme,"  is  in  effect  to  say,  "  that  ex- 
treme is  excluded  from  the  middle";  and 
hence  the  Dictum  de  Nullo  agrees  with  the 
Dictum  de  Diverso  in  asserting  that  two  terms, 
the  one  of  which  is  included  in  and  the  other 
excluded  from  a  common  middle  term,  are 
mutually  excluded. 

So  in  the  third  figure  the  dictum  is  equally 
applicable.  For  in  the  affirmative  forms  (Da- 
rapt  i,  Disamis,  and  Datisi]  it  is  asserted  that 
the  middle  is  contained  in,  and  in  the  negative 
forms  (Felapton,  Dokamo,  and  Feriso]  that  it 
is  excluded  from  one  of  the  extremes;  and  in 
both  it  is  asserted,  in  effect,  that  the  other  ex- 
treme is  partly  included  in  the  middle.  Hence 
the  former  come  directly  under  the  Dictum  de 


TRADITIONAL   LOGIC  115 

Omni,  and  the  latter  under  the  Dictum  de 
Nullo. 

That  the  dictum  agrees  with  the  Dictum  de 
Exemplo,  however,  cannot  be  said ;  for  that,  in 
terms,  merely  asserts  the  truism  that  "  two 
terms  which  contain  a  common  part  "  in  that 
respect  agree,  or,  "  if  one  contain  a  part 
which  the  other  does  not,"  to  that  extent 
differ.  But  it  gives  us  no  information  as  to 
the  principle  by  which  it  is  determined 
whether  the  two  terms  have  or  have  not  a 
common  part.  Whereas  the  dictum  of  Aris- 
totle explains  that  if  one  extreme  be  partly 
included  in  the  middle,  and  the  middle  be 
either  wholly  included  in  or  excluded  from  the 
other  extreme,  then  the  two  extremes  will  or 
will  not  agree  or  have  a  common  part,  as  the 
case  may  be. 

It  is  therefore  obvious  that  the  dictum  of 
Aristotle  applies  equally  to  all  syllogisms,  and 
that  to  invent  separate  canons  for  the  several  fig- 
ures is  unnecessary  and  productive  of  confusion. 

§  102.  THE  DICTUM  APPLICABLE  TO  SING- 
ULAR AND  OTHER  EQUATIOXAL  PROPOSI- 
TIONS.— It  has  also  been  objected  to  the 
dictum  by  several  logicians  that  it  is  not  ap- 
plicable to  syllogisms  in  which  the  terms  are 
singular,  or  to  other  syllogisms  composed  of 
equational  propositions;  which,  it  is  said,  are 
governed  by  a  different  regulating  principle, 


1 16  LOGIC 

viz.,  that  "  notions  equivalent  to  one  and  the 
same  third  notion  are  equivalent  to  each 
other"  (McCosh,  Logic,  pp.  126,  127).  But 
this  is  obviously  not  so.  For  an  individual 
may,  for  logical  purposes,  be  regarded  as  a 
class  (i.  e.,  a  class  of  one);  and  classes  that  are 
equal  to  each  other  mutually  include  each 
other.  Hence  the  dictum  applies  directly  to 
syllogisms  of  this  character;  and  we  may  al- 
ways express  such  a  syllogism,  e.  g. ,  Z  =  Y, 
Y  =  X  .'.  Z  =  X,  in  the  usual  form:  Z  is  Y, 
Y  is  X  .-.  Z  is  X. 

§  103.  OF  PROPOSED  IMPROVEMENTS  ox 
THE  DICTUM. — Other  objections  are  urged  to 
the  dictum  of  Aristotle  by  modern  logicians, 
and,  to  remedy  its  supposed  defects,  numerous 
new  dicta  or  canons  have  been  invented  to  take 
its  place.  But  these  will  be  found  on  examina- 
tion to  be  either  erroneous  or  merely  different 
and  less  satisfactory  statements  of  the  old 
dictum. 

In  at  least  this  fundamental  aspect  of  the 
subject  the  opinion  of  Kant  with  reference  to 
the  Old  Logic  must  be  accepted,  viz.,  that 
"  Since  Aristotle  it  has  not  had  to  retrace  a 
single  step,  and  to  the  present  day  has  not 
been  able  to  make  one  step  in  advance."  ' 

1  In  these  views  I  find  myself  supported  by  the  following 
judicious  observations  of  Professor  Jevons  : 

"During  the  last  two  or  three  years,"  he  observes,  "the 


TRADITIONAL  LOGIC  1 1/ 

3.  Rules  of  the  Syllogism 

§  104.  STATEMENT  OF  THE  RULES. — The 
following  rules,  with  the  fallacies  resulting  from 
their  violation,  are  given  by  logicians.  They 
are  all  obvious  deductions  either  from  the 
definition  of  the  syllogism  or  from  the  dictum 
of  Aristotle. 

(1)  Every    syllogism    has  three,    and    only 
three,  terms,  viz.,  the  Major,  the  Minor,  and 
the  Middle  term. 

The  violation  of  this  rule  is  called  the  Fal- 
lacy of  Four  Terms  (Quarternio  Terminorum). 
It  generally  results  from  the  ambiguity  of  a 
term,  and  indeed  can  hardly  occur  in  any 
other  way. 

(2)  Every  syllogism  contains  three,  and  only 
three,    propositions,    viz.,    the  Major  and  the 
Minor  premise  and  the  Conclusion. 

This  rule  can  be  violated  only  by  violating 
the  first  rule,  and  is  therefore  to  be  regarded 
as  superfluous. 

(3)  The   Middle  term   must   be  distributed 
once  at  least  in  the  premises. 

thought  has  constantly  forced  itself  on  my  mind,  that  the 
modern  logicians  have  altered  the  form  of  Aristotle's  proposi- 
tion without  making  any  corresponding  alterations  in  the 
dictum  or  self-evident  principle,  which  formed  the  fundamen- 
tal postulate  of  his  system.  Aristotle  regarded  the  proposi- 
tion as  stating  the  inclusion  of  one  term  or  class  within 
another  ;  and  his  axiom  was  perfectly  adapted  to  this  view 
(Pure  Logic,  p.  86). 


Il8  LOGIC 

The  violation  of  this  rule  is  called  the  Fallacy 
of  Undistributed  Middle,  as,  e.g.,  in  the  fol- 
lowing pseudo-syllogism:  X  is  Y,  Z  is  Y  .*.  Z 
is  X. 

(4)  No  term  must  be  distributed  in  the  con- 
clusion that  was  not  distributed  in  one  of  the 
premises. 

The  violation  of  this  rule  is  called  the  Fallacy 
of  the  Illicit  Process  of  the  Major  or  of  the 
Minor  term,  as  the  case  may  be,  as,  e.  g.,  in 
the  following  syllogism :  Y  is  not  X,  some 
Z  is  Y  . '.  Z  is  not  X,  —  Nations  capable 
of  self-government  should  not  be  despotically 
governed;  some  nations  are  capable  of  self- 
government;  no  nation  should  be  despotically 
governed, — which  is  a  case  of  illicit  process  of 
the  Minor  term  ;  or  as  in  the  following  syllo- 
gism: Y  is  X,  Z  is  not  Y  .*.  Z  is  not  X,— 
Anglo-Saxons  love  liberty,  Frenchmen  are 
not  Anglo-Saxons  .'.  Frenchmen  do  not  love 
liberty, — which  is  an  illicit  process  of  the  Major. 

(5)  From  negative  premises  nothing  can  be 
inferred. 

The  violation  of  this  rule  is  called  the  Fallacy 
of  Negative  Premises;  e.  g. ,  Y  is  not  X,  Z  is 
not  Y  .'.  Z  is  X  or  Z  is  not  X. 

(6)  If  one  premise  be  negative  the  conclusion 
must  be  negative;  and,   vice  versa,  to  prove  a 
negative  conclusion  one  of  the  premises  must 
be  negative. 


TRADITIONAL   LOGIC  1 19 

The  violation  of  this  rule  may  be  called  the 
Fallacy  of  Affirmative  Conclusion,  e.g.,  Y  is 
X,  Z  is  not  Y  .'.  Z  is  X. 

And  from  the  above  rules  may  be  deduced, 
as  corollaries,  the  following: 

(7)  From  two  particular  premises  no  conclu- 
sion can  be  drawn. 

(8)  If  one  premise  be  particular,  the  conclu- 
sion must  be  particular. 

4.   Of  Enthymemes  and  Sorites 

§  105.  OF  ENTHYMEMES. — An  Enthymeme 
is  a  syllogism  incompletely  stated,  but  in 
which  the  omitted  parts  are  understood  or  im- 
plied. Most  commonly  the  omitted  part  is  the 
major  premise,  which  is  then  said  to  be  sup- 
pressed, as,  e.  g. ,  "  Caesar  was  a  tyrant,  there- 
fore he  deserved  death,"  where  the  suppressed 
premise  is  the  major,  "  All  tyrants  deserve 
death."  Or  the  suppressed  premise  may  be 
the  minor,  as,  e.  g.,  "  Freemen  are  happy, 
therefore  the  English  are  happy,"  where  the 
suppressed  premise  is  the  minor,  "  English- 
men are  freemen." 

§  1 06.  OF  SORITES. — The  Sorites  consists  of 
a  string  of  syllogisms  in  the  first  figure,  in 
which  the  conclusion  of  each  is  made  the 
premise  of  the  next,  and  so  on,  till  finally  in 
the  conclusion  the  predicate  of  the  last  premise 


1 20  LOGIC 

is  predicated  of  the  subject  of  the  first,  as, 
e.  g.,  A  is  B,  B  is  C,  C  is  D,  D  is  E  .  \  A  is  E ; 
or,  to  give  a  concrete  example,  "  The  English 
are  brave,  the  brave  are  free,  the  free  are 
happy,  therefore  the  English  are  happy." 
Obviously  a  Sorites  may  always  be  resolved 
into  as  many  separate  syllogisms  as  it  has 
middle  terms,  as,  e.  g.,  in  the  above  example, 
the  first  into  three  and  the  last  into  two  syllo- 
gisms, as  follows: 

A  is  B  A  is  C  A  is  D 

B  is  C  C  is  D  D  is  E 

/.  A  is  C  .'.  A  is  D  .*.  A  is  E 

The  English  are  brave     The  English  are  free 
The  brave  are  free  The  free  are  happy 

.'.  The  English  are  free    .'.  The  English  are  happy. 


BOOK  II 
APPLIED  LOGIC 


121 


BOOK  II 
APPLIED  LOGIC 


PART  I 
OF  THE  METHOD  OF  LOGIC 


CHAPTER  VI 

OF   THE    LOGICAL   PROCESSES 

§  107.  OF  THE  METHOD  OF  LOGIC. — The 
logical  processes,  as  we  have  hitherto  con- 
sidered them,  consist  in  three  operations, 
namely,  Simple  Apprehension,  Judgment,  and 
Syllogism  or  Inference;  of  which  the  first  is 
an  analytical  process,  the  second  and  third 
synthetical.  Hence  the  logical  processes  may 
be  regarded  as  twofold,  and  as  consisting  in 
Analysis  and  Synthesis.  The  first  of  these, 
however,  is  not  confined  to  Simple  Apprehen- 
123 


124  LOGIC 

sion  or  analysis  of  terms,  but  extends  to  the 
analysis  of  propositions  and  syllogisms,  and  of 
extended  discourse  ;  of  which  the  elements  are 
syllogisms.  It  also  extends,  as  preparatory  to 
the  expression  in  logical  form  of  subjects  to  be 
investigated,  to  the  analysis  of  the  general 
facts  involved  and  the  determination  of  the 
questions  to  be  investigated.  The  logical 
method  consists  in  the  use  of  these  processes. 
§  108.  LOGICAL  DISTINGUISHED  FROM 
PHYSICAL  ANALYSIS  AND  SYNTHESIS. — The 
terms  analysis  and  synthesis  are  used  in  differ- 
ent senses,  according  to  the  subject-matter  to 
which  they  are  applied.  Of  these,  two  princi- 
pal kinds  may  be  distinguished,  which  may  be 
called,  respectively,  physical  and  logical — the 
former  dealing  with  physical  substances,  the 
latter  with  notions  or  concepts.  Of  the  former 
kind,  the  most  instructive  illustration  is  pre- 
sented by  chemistry ;  where  these  processes  are 
applied  directly  to  matter,  which  is  analyzed 
by  separating  its  elements,  and  synthesized  by 
rearranging  those  elements  so  as  to  form  new 
compound  substances.  These  processes  are 
indeed  essentially  different  in  nature  from  the 
processes  with  which  we  are  now  concerned, 
yet  the  analogy  between  the  two  is  almost 
perfect;  and  hence,  in  chemical  analysis  and 
synthesis,  we  find  the  best  illustration  of  the 
nature  of  analysis  and  synthesis  of  notions  or 


THE  LOGICAL  PROCESSES  12$ 

terms,  by  which — in  a  way  very  similar  to  the 
analysis   and    synthesis  of  material  bodies  — 
notions  are  analyzed  into  elementary  notions, 
and  these  again  synthesized  into  compound. 

§  109.  OF  THE  WORLD  OF  THINGS  AND 
THE  WORLD  OF  THOUGHT. — The  world  of 
things  is  made  up  of  actual  things  or  sub- 
stances; the  world  of  thought,  of  concepts  or 
notions.  There  is  between  the  two  a  regular 
correspondence,  i.  e.,  a  correspondence  deter- 
mined by  invariable  law,  and  yet  the  two  are 
clearly  distinct.  For  it  is  obvious  that  things 
themselves  cannot  be  in  the  mind  but  only, 
notions  or  concepts  of  them.  These,  as  we 
have  seen,  if  real  or  true,  must  correspond, 
either  directly  or  indirectly,  with  the  things 
which,  or  the  attributes  of  which,  they  are 
supposed  to  denote  (§  29,  n.).  Where  the 
correspondence  is  indirect,  the  thing  denoted 
is  a  guast-thing  only,  and  cannot  be  distin- 
guished from  the  notion  itself;  but  where  the 
correspondence  is  direct,  there  is  a  real  thing 
corresponding  to  the  notion,  and  we  may 
either  regard  the  notion  or  the  thing  as  the 
significate  of  the  term  (§  37,  n.);  though  even 
in  this  case  it  is  really  the  notion,  not  the 
thing,  that  we  have  in  mind  (§  38,  n.).  So 
that  it  may  be  said  that  Logic,  and  science 
generally,  deal  directly  with  concepts  or  no- 
tions only — that  is  to  say,  with  the  world  of 


126  LOGIC 

thought  only,  and  with  the  world  of  real  things 
only  indirectly. 

§  1 10.  LOGIC  AS  THE  DOCTRINE  OF  SIGNS 
(SEMEIOTIKE). — But  the  notions  or  thoughts 
dealt  with  by  Logic  are  not  the  evanescent 
thoughts  of  the  individual,  but  the  common 
notions  of  mankind  embodied  in  language 
(§  30).  Hence,  as  we  have  observed,  Logic 
is  exclusively  conversant  with  language,  or 
rather,  more  specifically,  with  terms  and  their 
various  ratiocinative  combinations  (§§  14,  16) 
— that  is  to  say,  with  the  signs  of  the  notions 
or  concepts  and  of  their  relations  ;  which 
cannot  be  dealt  with,  at  least  to  any  con- 
siderable extent,  except  by  means  of  the 
vocables  by  which  they  are  signified.  Hence 
Logic  must  be  regarded,  in  its  direct  scope,  as 
dealing  with  the  signs  by  which  notions  and 
their  relations  are  expressed — precisely  as,  in 
the  mathematics,  the  subject-matter  dealt  with 
consists  of  the  signs  of  numbers  and  of  their 
relations.  In  both  cases,  therefore,  though 
the  ultimate  object  of  Logic  is  to  determine 
the  notions  expressed  in  terms  and  their  re- 
lations, and  ultimately  the  nature  and  the 
relations  of  the  things  corresponding  to  the 
notions,  yet  this  is  effected  by  means  of  signs, 
which,  therefore,  constitute  the  immediate 
subject  dealt  with.  Hence  Locke  was  quite 
right  in  conceiving  that  a  science  of  this  char- 


THE  LOGICAL  PROCESSES  12? 

acter  is  indispensable,  and  in  giving  it  the  ap- 
propriate name  of  "  Semeiotike,  or  the  Doctrine 
of  Signs,"  though  quite  wrong  in  supposing 
that  this  would  be  a  new  kind  of  Logic.1 

§  in.  THE  METHOD  OF  LOGIC  RESUMED. 
—By  the  method  of  Logic  is  meant  the  method 
of  its  use  in  reasoning,  or,  in  other  words,  the 
method  of  ratiocination,  or  explicit  reasoning. 
This,  as  we  have  said,  consists  in  two  processes 
or  operations,  namely,  Analysis  and  Synthe- 
sis, i.  e.,  of  language  (§  107).  By  analysis  is 
meant  the  separation  of  a  whole — whether  con- 
sisting of  a  term,  proposition,  syllogism,  or 
larger  discourse,  or  of  the  general  problem 
or  subject  to  be  investigated  —  into  its  com- 
ponent parts;  by  synthesis,  the  comparison  (or 
placing  together)  of  any  of  the  elements  of 
reasoning,  with  a  view  to  determining  their  re- 
lations; that  is  to  say,  in  the  comparison  of 
terms,  in  order  to  form  a  judgment  of  their 
relations — of  propositions,  in  order  to  make  an 
inference;  and  of  syllogisms,  in  order  to  make 
an  extended  ratiocination  or  argument.  An- 
alysis and  synthesis  are,  therefore,  each  the 
converse  of  the  other. 

§  ii2.    MODES  OF   APPLICATION  OF  THE 

1  "  The  consideration  then  of  ideas  and  words,  as  the  great 
instruments  of  knowledge.  .  .  .  Perhaps  if  they  were 
distinctly  weighed  and  duly  considered,  they  would  afford  us 
another  sort  of  Logic  and  critic  than  what  we  have  hitherto 
been  acquainted  with  "  (see  Appendix  N). 


128  LOGIC 

LOGICAL  PROCESSES.— In  each  stage  of  ratio- 
cination analysis  and  synthesis  are  used  con- 
jointly, and  each  is  equally  indispensable.  The 
order  in  which  their  applications  occur,  how- 
ever, differs  according  to  the  purpose  we  have 
principally  in  view,  which  may  be  either  In- 
vention or  Criticism;  that  is  to  say,  either  (i) 
the  Discovery  of  Truth,  or  (2)  the  Criticism  or 
Judgment  of  what  is  supposed  or  alleged  to  be 
true;  or,  in  other  words,  the  verification  of 
truth  and  the  detection  of  fallacy.  Of  these 
two  aspects  of  Logic,  the  latter  is  commonly, 
and  perhaps  rightly,  regarded  as  the  more  im- 
portant, or,  at  least,  as  of  the  greater  practical 
utility.  But  the  former,  though  commonly 
undervalued,  is  hardly  of  less  utility  or  less 
fruitful  of  practical  results. 

§  113  (i)  INVENTION. —  The  operations  of 
Logic,  regarded  as  an  Instrument  or  Organon 
of  Invention,  consist  in  the  analysis  and  conse- 
quent apprehension  of  terms  (Simple  Appre- 
hension), and  in  the  discovery  or  invention  of 
judgments  and  of  syllogisms,  and  of  argu- 
ments—  which  are  composed  of  syllogisms; 
which  is  effected  by  synthesis;  and  the  process 
of  ratiocination  proceeds  in  this  order,  i.  e. , 
from  the  term  to  the  proposition,  from  the 
proposition  to  the  single  syllogism,  and  from 
that  to  the  extended  discourse  or  argument. 

§  114.    OF    THE    DISTINCTION    BETWEEN 


THE  LOGICAL  PROCESSES  12$ 

ORIGINAL  AND  COMMONPLACE  THOUGHT.— 
Where  the  notions  expressed  in  terms  are  dis- 
tinctly apprehended,  and,  with  reference  to  all 
terms,  to  the  extent  they  are  apprehended,  the 
relations  between  them  are  readily  perceived, 
and  indeed  spontaneously  present  themselves. 
Hence  with  such  notions  men  reason  with 
facility  and  accuracy;  and  thus  originate  the 
numerous  opinions  that  are  common  to  man- 
kind, or  common  at  least  to  men  generally 
under  the  same  conditions  of  environment; 
and  also  those  that  are  common  to  large  classes 
of  men.  Of  such  opinions — which  may  be  ap- 
propriately named  Commonplace — the  current 
literature  and  thought  of  the  day  largely,  or, 
we  may  say  almost  exclusively,  consist.  Hence 
the  effect  of  current  thought  and  discourse 
is  simply  to  disseminate  such  opinion  more 
widely,  and  thus  gradually  to  develop  and 
consolidate  Common  Opinion,  or  Conscience, 
which  has  been  called  by  the  Greeks  Nomos, 
and  by  some  philosophers  Common  Sense. 
This,  indeed,  is  a  useful  and  essentially  neces- 
sary function;  for  it  is  recognized  by  political 
writers  generally  that  opinion  is  the  ultimately 
controlling  force  in  politics,  and  that  when  it 
becomes  universal  and  inveterate,  it  is  supreme. 
But  current  thought  is  marked  by  an  essential 
characteristic,  or,  we  may  say,  defect — namely, 
that  it  is  incompatible  with  originality,  either 


130  LOGIC 

in  the  acquisition  of  new  truths  or  in  the  ap- 
preciation of  original  thought  in  others.  Hence 
it  has  happened,  throughout  the  history  of 
mankind,  that  the  results  of  original  thought 
meet  with  almost  insuperable  obstacles  to  their 
reception ;  and  that,  even  where  they  have  es- 
tablished their  footing,  they  pass  into  the 
hands  of  commonplace  thinkers,  who  treat 
them  after  their  own  methods.  Hence  the 
original  works  of  great  thinkers,  with  their 
methods  of  thought  and  expression,  and  the 
vivifying  effect  of  actual  example,  are  sub- 
merged by  the  newer  and  inferior  literature. 

On  the  other  hand,  where  the  Analytical 
Method  is  rigorously  applied  to  all  forms  of 
discourse,  and  especially  when  it  is  applied  to 
the  notions  or  concepts  embodied  in  terms, 
numerous  delicate  and  important  but  unsus- 
pected relations  between  the  notions  thus  de- 
termined suggest  themselves.  For  in  this  also 
logical  is  like  chemical  analysis,  where, 
by  the  resolution  of  compound  substances, 
thousands  of  relations  between  them  and 
between  the  elements  of  which  they  are 
composed  are  developed  and  disclosed.  The 
perception  of  these  unsuspected  relations  con- 
stitutes originality,  which  is  but  another  name 
for  logical  power.  Nor  is  this  originality  any- 
where more  conspicuously  displayed  than 
where  men  of  original  genius,  as,  e.  g.,  Bacon 


THE  LOGICAL  PROCESSES  131 

in  \\isEssays,  deal  with  commonplace  subjects.1 
Hence  the  use  of  Logic  as  an  Instrument  of 
Invention  cannot  be  too  highly  appreciated, 
for  in  the  capacity  to  use  Logic  in  this  way, 
or,  in  other  words,  in  the  capacity  to  apprehend 
the  whole  significance  of  terms  by  resolving 
them  into  their  elements,  lies  the  essential  dif- 
ference between  the  Original  and  the  Common- 
place Thinker.1 

§  115  (2)  CRITICISM. — In  this  aspect  Logic 
may  be  likened  to  the  touch  of  Ithuriel's  spear.2 

1  Where  terms  are  clearly  defined  and  analyzed  into  their 
constituent  elements, — that  is  to  say,  thoroughly  apprehended, 
— innumerable  relations  between  them  are  intuitively  per- 
ceived ;  and  thus,  by  the  use  of  this  method,  we  are  led  on, 
as  Locke  says  in  a  passage  cited  (supra  §  6,  n.),  "  from 
very  plain  and  easy  beginnings,  by  gentle  degrees  and  a  con- 
tinued chain  of  reasonings,  ...  to  the  discovery  and 
demonstration  of  truths  that  appear,  at  first  sight,  beyond 
human  capacity."  This  it  was,  probably,  that  inspired  the 
beautiful  hymn  of  Newman  : 
"  Lead  on,  Heavenly  Light ;  amid  the  encircling  gloom, 

Lead  Thou  me  on  "  ; 

which  may  be  very  properly  regarded  as  in  reality  an  ode  to 
the  divine  gift  of  Intuition  —  the  only  source  of  perfect 
knowledge. 

2     "Him  there  they  found 
Squat  like  a  toad  at  the  ear  of  Eve. 

Him  thus  intent  Ithuriel  with  his  spear 

Touched  lightly  ;  for  no  falsehood  can  endure 

Touch  of  celestial  spear,  but  returns 

Of  force  to  its  own  likeness  ; 

So  started  up  in  his  own  shape  the  fiend," 


132  LOGIC 

Commonly  the  reasoning  processes  operate 
unconsciously  and  automatically,  and  the  rea- 
soning is  more  or  less  inaccurate,  and  hardly 
ever  consecutive  or  logically  coherent.  As 
observed  in  the  Introduction,  proposition  fol- 
lows proposition  in  our  minds,  suggested  by 
various  principles  of  association,  such,  e.  g.,  as 
experience,  habit,  authority,  inclination,  etc. ; 
and  thus  the  great  mass  of  our  opinions  and 
beliefs — which  we  very  erroneously  call  our 
knowledge — comes  to  us  we  know  not  how. 
Nor,  however  firmly  we  may  be  convinced  of 
them,  or  however  passionately  we  may  assert 
them,  have  we  any  just  assurance  of  their 
truth;  nay,  it  is  matter  of  familiar  knowledge 
that  they  are  all  mingled  with  error.  Hence, 
we  concluded,  the  necessity  is  apparent  for 
some  test  or  criterion  by  which  to  judge  them ; 
and  this,  except  the  sometimes  painful  test  of 
experience,  can  be  nothing  else  than  Logic. 
In  its  critical  aspect,  therefore,  Logic  is  indis- 
pensable, not  only  to  save  us  from  errors  and 
absurdities,  but  to  distinguish  real  from  unreal 
knowledge,  and  to  give  us  assurance  of  the 
former  (§  7  et  seq.\  Without  it,  except  in 
concrete  matters,  no  man  can  know  whether 
he  is  right  or  wrong;  and  while  some,  happily 
born,  learn  by  practice  the  application  and 
use  of  the  logical  processes,  the  great  mass  of 
mankind,  for  the  lack  of  Logic,  go  through  life 


THE  LOGICAL  PROCESSES  133 

mistaking  falsehood  and  even  nonsense  for 
knowledge,  and  yet  firmly  convinced  of  their 
wisdom  and  of  the  folly  of  those  who  differ 
from  them.  Hence,  in  the  critical  aspect  of 
Logic,  the  order  of  applying  the  logical  pro- 
cesses is  the  reverse  of  what  it  is  in  the  use  of 
Logic  as  an  organon  or  instrument  of  inven- 
tion. There  the  order  is  to  commence  with 
the  analysis  of  the  term,  and  then  to  proceed 
to  the  synthesis  of  terms  in  propositions, 
syllogisms,  and  extended  discourse;  here  we 
commence  with  the  complex  result,  and  by 
analysis  resolve  it  into  its  elements. 

§  116.  OF  THE  USE  OF  ANALYSIS  GENER- 
ALLY.— In  the  use  of  Logic,  whether  for  in- 
vention or  for  criticism,  analysis  and  synthesis 
are  equally  indispensable;  but  the  latter,  after 
the  former  has  been  effected,  is  largely  a 
natural  and  spontaneous  process,  and  presents 
but  little  difficulty  in  its  performance.  On  the 
other  hand,  analysis,  while  to  a  certain  extent 
also  spontaneous,  requires,  for  its  efficient  per- 
formance, the  most  vigorous  and  protracted 
exertion  of  the  mental  faculties, —  as,  e.  g.,  in 
the  mathematics, —  and  hence  is  at  once  the 
most  important  and  the  most  difficult  of  the 
logical  processes.  It  will  therefore  require 
our  special  attention. 

We  have  distinguished  between  the  inven- 
tional  and  the  critical  functions  of  Logic,  and 


134  LOGIC 

also  with  reference  to  the  use  of  the  logical 
processes  as  applied  in  the  performance  of  the 
one  or  the  other  function ;  and  with  reference 
to  invention,  we  have  regarded  the  function  of 
analysis  as  limited  to  the  analysis  of  terms, 
with  a  view  to  an  apprehension  of  the  notions 
expressed  by  them.  In  practice,  however,  it 
is  difficult  to  distinguish  between  the  uses  of 
analysis  for  invention  and  for  criticism.  For, 
as  we  have  observed,  the  human  mind  is  so 
constituted  that  the  synthetical  process  is 
performed  spontaneously  and  involuntarily. 
Hence  there  is  no  subject  that  can  present 
itself  for  our  investigation  which  we  can  ap- 
proach unembarrassed  by  opinions  already 
formed;  and,  indeed,  until  such  opinions  or 
theories  are  formed,  the  process  of  investiga- 
tion cannot  commence.  Hence,  as  is  generally 
recognized,  the  method  of  scientific  investiga- 
tion must  consist  largely  in  the  forming  of 
theories  and  their  subsequent  investigation. 
We  may  distinguish,  however,  between  our 
own  theories,  either  accidentally  formed  or 
formed  for  the  purpose  of  the  investigation  of  a 
proposed  subject,  and  the  theories  formally  pro- 
pounded by  others,  either  in  writing  or  speech  ; 
and  we  may  conveniently  regard  the  former  as 
belonging  to  the  function  of  invention,  and  the 
latter  to  that  of  criticism.  The  latter,  as  being 
the  simpler  subject,  will  be  first  considered. 


THE  LOGICAL  PROCESSES  135 

§  117.  (i)  OF  THE  USE  OF  ANALYSIS  IN 
CRITICISM. —  In  this  case  the  function  of 
analysis  extends  to  the  analysis  of  all  forms 
of  language,  from  the  term  to  the  extended 
discourse  or  argument;  and,  as  we  have  ob- 
served, it  commences  with  the  latter,  which  is 
in  fact  the  most  difficult  task.  For  here  it  is 
necessary  to  determine  from  the  loose  and  in- 
accurate expressions  of  ordinary  disquisition 
the  precise  nature  of  the  conclusions  asserted 
and  of  the  arguments  used  to  establish  them ; 
and  this  task  is  always  difficult,  and  sometimes 
impossible.  When  these  matters  have  been 
determined  it  will  be  necessary  also  to  analyze 
carefully  every  syllogism,  proposition,  or  term 
involved  in  the  course  of  the  reasoning.  But 
this  in  general,  to  the  trained  logician,  presents 
but  little  difficulty. 

§  118.  (2)  OF  THE  USE  OF  ANALYSIS  IN  IN- 
VENTION.— Strictly  speaking,  this  perhaps  ex- 
tends only  to  the  analysis  of  the  term  with  a 
view  to  simple  apprehension,  and  in  a  previous 
passage  we  have  so  regarded  it.  But  before 
this  task  can  be  approached,  it  is  necessary  for 
us  to  determine  the  nature  of  the  precise  ques- 
tions to  be  investigated  ;  and  this  will  require  an 
analysis  of  the  facts  involved  in  the  investiga- 
tion, and  also  of  the  opinions  or  theories  with 
regard  to  those  facts  casually  existing  in  the 
mind.  For,  as  will  be  explained  more  fully  in 


136  LOGIC 

the  next  chapter,  the  questions  demanding  in- 
vestigation are  in  general  determined  by  the 
nature  and  the  conditions  of  the  problems 
involved ;  and  it  is  essential  to  a  rational  in- 
vestigation that  the  issues  thus  involved  be 
clearly  ascertained.  When  the  issues  or  ques- 
tions are  thus  determined  and  logically  ex- 
pressed, our  investigation  is  then  narrowed  to 
the  determination  of  the  truth  of  one  of  two 
alternative  propositions,  which  are  called  the 
thesis  and  the  anti-thesis,  and  of  which  one  or 
the  other  must  be  true;  and  thus  our  task  is 
in  general  greatly  facilitated.  The  use  of  this 
sort  of  analysis  finds  its  best  illustration  in  the 
practice  of  the  lawyers,  with  whom  it  is  an  im- 
perative rule  that  the  first  step  in  the  investi- 
gation of  a  case  must  consist  in  settling  the 
issues.  In  ordinary  discourse  this  task  is 
almost  always  neglected,  and,  as  will  be  seen 
as  we  proceed,  this  is  one  of  the  most  fruitful 
sources  of  fallacy. 

§  119.  OF  ANALYSIS  AND  SYNTHESIS  GEN- 
ERALLY.— This  subject  is  one  of  extreme  im- 
portance, and  to  the  advanced  student  should 
constitute  one  of  the  principal  subjects  for  his 
meditations;  but  for  the  purposes  we  have  in 
view  it  may  be  sufficiently  developed  by  a 
statement  of  the  practical  rules  by  which  the 
reasoner  should  be  governed,  which  will  be 
given  at  length  in  the  next  chapter. 


CHAPTER  VII 

THE    RULES   OF   LOGIC 

I 
OF    THE    RULES    OF    LOGIC    GENERALLY 

§  120.  SCOPE  OF  THE  RULES  OF  LOGIC.— 
According  to  the  view  we  have  taken  in  this 
essay,  inference  is  only  one  of  the  processes  of 
ratiocination.  Judgment  is  also  a  ratiocinative 
process,  and,  like  inference,  must  have  its  rules 
by  which  false  or  pretended  judgments  may  be 
distinguished  from  the  real.  Moreover,  where 
our  reasoning  is  not  apodictic,  we  have  to  use 
assumed  propositions,  or  assumptions,  as  prem- 
ises ;  and  though  it  is  said  that  Logic  is  not 
concerned  with  the  truth  or  falsity  of  these,  yet 
this  is  true  only  in  a  qualified  sense.  For 
where  the  falsity  of  such  propositions  can  be 
detected  by  logical  processes, — i.  e.,  by  defini- 
tion, judgment,  and  inference, — it  is  the  func- 
tion of  Logic  to  condemn  and  reject  them ; 
precisely  as  in  the  case  of  self-contradictory 


138  LOGIC 

propositions  or  propositions  otherwise  absurd 
on  their  face.  And  in  all  cases  it  is  its  func- 
tion to  determine  the  logical  character  of  an 
assumed  premise,  as  being  an  assumption  or 
hypothesis,  and  not  a  judgment. 

§  121.  TWOFOLD  DIVISION  OF  THE  RULES 
OF  LOGIC. — We  propose,  therefore,  to  regard 
the  rules  of  Logic  as  legitimately  extending  to 
all  the  processes  of  ratiocination  ;  and  hence  as 
including  all  rules  necessary  to  direct  us  in  the 
right  use  of  terms  as  instruments  of  ratiocina- 
tion. They  will  include,  therefore,  not  only 
the  rules  directly  governing  the  process  of  in- 
ference, but  also  those  governing  the  statement 
of  the  premises.  The  latter  —  which  will  first 
be  considered  —  will  be  called  the  "  Rules  of 
Judgment,'"  the  former,  the  "  Rules  of  In- 
ference." 

§  122.  RULES  OF  JUDGMENT. — The  rules  of 
judgment  have  for  their  object,  not  the  form- 
ing of  right,  but  the  prevention  of  wrong  judg- 
ments. Judging  is  a  natural  and  involuntary 
operation  of  the  mind.  But  in  the  ordinary 
processes  of  the  mind  we  are  apt  to  go  astray 
in  our  judgments;  and  the  object  of  the  rules 
of  judgment  is  to  guard  against  this  infirmity 
by  preventing  false  judgments,  or,  where  they 
occur,  by  detecting  them. 

§  123.  RULES  OF  INFERENCE. — The  rules 
of  the  syllogism  given  in  a  previous  chapter 


THE   RULES  OF  LOGIC  139 

cover  all  cases  of  inference  except  conversion 
per  accidens.  But  these  rules  are  needlessly 
complex,  and  may  be  advantageously  replaced 
by  the  rules  of  substitution,  which  include 
all  inferences  whatever,  and  are  simpler  both  in 
their  expression  and  application  than  the  old 
rules,  of  which  they  are  but  another  expres- 
sion. The  rules  of  the  syllogism,  however, 
are  of  such  familiar  use  by  logicians,  and  are  so 
wrought  into  the  terminology  and  literature  of 
Logic,  that  a  familiar  acquaintance  with  them 
is  essential  to  the  logical  student;  for  whom 
also  it  will  be  necessary  to  recognize  clearly 
the  substantial  identity  of  the  two  processes. 

§  124.  FALLACIES  OF  THE  SYLLOGISM,  ALL 
RESOLVABLE  INTO  FALLACIES  OF  SUBSTITU- 
TION.— This  is  especially  important  with  refer- 
ence to  the  violations  of  the  rules  of  the 
syllogism,  or,  as  they  are  called,  the  fallacies 
of  the  syllogism  (§104  ct  scq.\  These  are 
of  frequent  occurrence,  and  are  familiarly 
known  by  technical  names;  and  as  these  have 
become  firmly  established  in  logical  termi- 
nology by  a  use  of  many  centuries,  they  must, 
of  course,  be  retained.  It  will  be  of  advantage 
to  the  student,  therefore,  to  have  pointed  out 
to  him  that  all  these  fallacies  are  simply  cases 
of  illicit  substitution ;  which  can  be  readily 
shown. 

Thus,   e.  g<,   the    fallacy   of   an    ambiguous 


I4O  LOGIC 

middle  term  (Quarternio  Terminorutri)  consists 
simply  in  the  substitution  of  a  new  term,  hav- 
ing the  same  verbal  sign  as  in  the  original,  but 
a  different  meaning — as  in  the  examples  given. 

The  case  of  undistributed  middle — as,  e.  g. , 
"  X  is  Y,  Z  is  Y  .-.  Z  is  X  "  -  consists  in  the 
illicit  substitution  of  species  for  genus  in  the 
predicate  of  an  affirmative  proposition  (i.  e.,  X 
for  Y  in  the  minor  premise). 

In  the  case  of  illicit  process  of  the  minor  term, 
—  as,  e.  g.,  "  Y  is  not  X,  some  Z  is  Y  .'.  Z  is 
notX," — genus  is  illicitly  substituted  for  species 
in  the  subject  of  an  affirmative  proposition 
(i.  e,,  Z  for  "  Some  Z  "  in  the  minor  premise). 

In  the  case  of  illicit  process  of  the  major, — as, 
e.  g.,  "  Y  is  X,  Z  is  not  Y  .-.  Z  is  not  X,"— 
genus  is  illicitly  substituted  for  species  in  the 
predicate  of  a  negative  proposition  (i.  e.,  X  for 
Y  in  the  minor  premise). 

In  the  case  of  negative  premise,  if  the  con- 
clusion be  affirmative, — as,  e.  g. ,  "  Y  is  not  X,  Z 
is  not  Y  .'.  Z  is  X," — genus  is  substituted  for 
species  in  the  predicate  of  a  negative  proposi- 
tion (i.  e.,  Not-X  for  Y  in  the  minor  pre- 
mise). If  the  conclusion  be  negative, — as,  e.g., 
"  Y  is  not  X,  Z  is  not  Y  .  •.  Z  is  not  X,"— the 
fallacy  will  consist  in  the  illicit  substitution  of 
one  for  another  of  two  unrelated  terms  (i.  e., 
X  for  Y);  and  the  same  will  be  true  of  the 
other  cases,  if  any  there  be. 


THE  RULES  OF  LOGIC  141 

§125.  THE  LAWS  OF  THOUGHT. — The 
rules  of  Logic  are  founded  upon  what  are 
called  the  primary  Laws  of  Thought,  viz.  : 
(i)  the  Law  of  Identity  (or  rather  the  Law  of 
Equivalence);  (2)  the  Law  of  Contradiction; 
and  (3)  the  Law  of  Excluded  Middle;  the  first 
of  which  governs  the  process  of  Inference,  the 
last  two,  that  of  the  Judgment.  The  corre- 
sponding fallacies  consist  in  their  violation. 

These  laws  may  be  enunciated  in  a  form  to 
make  them  of  practical  utility,  as  follows: 

(i)  THE  LAW  OF  IDENTITY. 

Significates  (i.  e.,  things  or  quasi-things)  re- 
main the  same  though  denoted  by  different 
terms. 

Hence  terms  denoting  the  same  significates 
may,  to  the  extent  of  their  equivalence,  be 
used  interchangeably,  i.  e.,  the  one  substituted 
for  the  other. 

The  mathematical  axiom  that  "  things  equal 
to  the  same  thing  are  equal  to  each  other  "  is 
merely  a  special  application  of  this  principle, 
its  meaning  being  simply  that  terms  denoting 
the  same  class  of  significates  are  equivalent  to 
each  other. 

It  is  obvious,  therefore,  that  this  law  is  not 
adequately  stated  (as  is  sometimes  said)  by  the 
equation,  A  =  A,  but  rather  by  the  equation, 
A  =  B;  both  terms  being  supposed  to  denote 
the  same  class  of  significates,  and  the  term  B 


142  LOGIC 

to  be  either  A,  or  any  other  vocable  or  sign 
denoting  the  same  significates. 

(2)  THE    LAW    OF    CONTRADICTION,    OR 
RATHER  THE  LAW  OF  NON-CONTRADICTION. 

A   term,  and  its  negative,  or  contradictory, 
cannot  be  predicated  universally  of  any  term. 
This  law  and  the  next  are  often  misstated. 

(3)  THE  LAW  OF  EXCLUDED  MIDDLE. 

Of  two  contradictory  propositions,  one  must  be 
true ;  or  symbolically  :  ' ' Either  A  is  It,"  or 
' '  Some  A  is  not  B. "  l 

II 

RULES    OF    JUDGMENT 

§126.   Rule  I.   TERMS  TO  BE  SIGNIFICANT. 

In  every  logical  proposition — by  which  is  meant 
every  proposition  to  be  used  in  ratiocination — the 
terms  must  be  significant,  i.  e.,  must  have  defi- 
nite signification. 

This  rule  follows  from  the  definition  of  the 
term  and  of  the  proposition ;  for  unless  the 
word  or  vocable  has  such  definite  signification 
there  is  no  name,  and  consequently  no  term  or 
proposition,  or  valid  ratiocination.  The  viola- 
tion of  this  rule  may  be  called  the  Fallacy  of 
Non-significance  or  Nonsense. 

Rule  II.    TERMS  TO  BE  RIGHTLY  DEFINED. 

Terms  used  in  ratiocination  must  not  only  have 

1  V.,  supra,  §  90. 


THE  RULES  OF  LOGIC  143 

a  definite  signification,  but  the  signification 
must  be  legitimate,  i.  e.,  they  must  not  be  falsely 
defined.  This  implies  (i)  that  a  term  shall  not 
be  used  in  an  improper  sense,  i.  e. ,  in  a  sense  not 
permitted  by  the  usage  of  the  language '  /  and 
(2)  that  the  term  shall  be  so  defined  as  to  signify 
a  real  concept ;  or,  at  least,  that  the  contrary 
shall  not  affirmatively  appear. 

The  violation  of  this  rule  will  be  called  the 
Fallacy  of  False  Definition. 

Rule  III.  PREMISES  NOT  TO  BE  ILLICITLY 
ASSUMED. 

A  proposition  that  is  obviously  untrue,  or  that 
can,  on  logical  principles,  be  affirmatively  shown 
to  be  untrue,  cannot  be  legitimately  used  as  a 
premise. 

The  violation  of  this  rule  is  called  the  fallacy 
of  "  Begging  the  Question,"  or  Petitio  Prin- 
cipii ;  and  this  and  the  fallacies  resulting  from 
the  violation  of  Rules  I.  and  II.  may  be 
classed  together  under  the  general  head  of 
Illicit  Premises. 

Rule  IV.  PREMISES  TO  CORRESPOND  TO 
THE  THESIS  OR  ISSUE. 

In  all  ratiocination — if  designed  to  be  fruitful 

1  The  unnecessary  use  of  a  term  in  a  sense  not  justified  by 
usage  is  commonly  indicative  either  of  mental  incapacity  or 
fallacious  intent ;  and  should  therefore  be  forbidden,  as  to 
children  \ve  forbid  the  use  of  deadly  weapons,  or  to  all  the 
possession  of  counterfeiters'  tools. 


144  LOGIC 

— the  premises,  and,  consequently,  also  the  con- 
clusion, must  correspond  to  the  Thesis  or  Issue, 
^whether  that  be  expressed  or  understood,  or 
merely  determined  by  the  conditions  of  the 
problem. 

By  the  thesis  is  meant  the  proposition  to  be 
demonstrated ;  by  the  issue  t  the  thesis  and  the 
anti-thesis,  or  contradictory,  considered  to- 
gether with  a  view  of  determining  whether  the 
one  or  the  other  is  true. 

With  regard  to  nearly  all  subjects  presented 
to  us  for  investigation  the  material  question  at 
issue  is  more  or  less  definitely  determined  by 
the  conditions  of  the  problem  ;  and  hence  it  is 
said,  "  A  prudent  questioning  is  a  kind  of  half 
knowledge  ' '  (Prudens  interrogatio  est  dimidium 
sapientice}.  Where  the  issue  is  thus  determined, 
it  constitutes  the  real  issue,  or  thesis  and  anti- 
thesis of  the  problem.  In  other  cases  it  must 
be  determined  by  agreement,  or  by  actual  in- 
tention, either  expressed  or  understood.  In 
many  cases  it  is  not  formally  stated,  but  we 
ascertain  it,  for  the  first  time,  from  the  use 
made  of  the  conclusion. 

The  fallacy  resulting  from  a  violation  of  this 
rule — if  we  assume  there  is  no  fallacy  in  the 
inference — will  necessarily  involve  a  departure 
from  the  thesis  or  issue,  both  in  the  premises 
and  in  the  conclusion.  With  regard  to  the 
premises,  it  is  called  the  fallacy  of  Mistaking 


THE  RULES  OF  LOGIC  145 

the  Issue ;  with  regard  to  the  conclusion,  that 
of  Irrelevant  Conclusion;  and  in  either  case, 
Ignoratio  Elenchi. 

Ill 

RULES   OF   INFERENCE 

§  127.  All  inference,  as  we  have  observed, 
may  be  resolved  into  the  process  of  substituting 
for  terms  other  terms  of  equivalent  ratiocina- 
tive  value.  There  is  an  apparent  exception  in 
the  case  of  conversions  of  propositions,  but  the 
exception  is  only  apparent  (§  79).  To  conform 
to  usage,  however,  the  rule  for  conversion  will 
be  given,  though  in  fact,  as  explained,  the  illicit 
conversion  of  a  proposition  is  simply  a  case  of 
illicit  substitution  of  terms. 

Rule  V.     CONVERSIONS  TO  BE  ILLATIVE. 

A  conversion,  to  be  legitimate,  must  be  illative, 
i.  e, ,  the  truth  of  tlie  converted  must  be  implied 
in  the  original  proposition. 

The  violation  of  this  rule  may  be  called  the 
Fallacy  of  Conversion,  or  simply  Illicit  Conver- 
sion. It  can  occur  only  in  the  simple  conver- 
sion of  a  universal  affirmative  or  a  particular 
negative  proposition  (e.  g.,  "  Y  is  X,"  "  Some 
Y  is  not  X  ").  In  the  former  case  the  fallacy 
will  consist  in  the  substitution  of  genus  for 
species  (X  for  Y)  in  the  subject,  and  of  species  for 
genus  (Y  for  X)  in  the  predicate  of  a  universal 


146  LOGIC 

affirmative  proposition,  thus  doubly  violating 
the  first  rule  of  substitution.  In  the  lat- 
ter ("  Some  Y  is  not  X  ")  X  is  substituted  for 
Y  in  the  subject,  and  Y  for  X  in  the  predi- 
cate, though  neither  is  necessarily,  and  one  at 
least  cannot  be,  a  species  of  the  other;  which 
is  a  violation  of  the  next  rule. 

Rule  VI.  EQUIVALENCE  OF  TERMS  TO  BE 
OBSERVED. 

In  all  substitutions  the  substituted  term  must 
be  equivalent  in  signification — i.  e.,  equivalent  in 
ratiocinative  value — to  the  term  for  which  it  is 
substituted. 

The  violation  of  this  rule  by  the  substitution 
of  a  new  term  is  called  the  Fallacy  of  Illicit 
Substitution. 

The  rule  will  cover  all  cases  of  legitimate 
substitution  of  terms  whatever  ;  but  it  is  ob- 
vious, where  an  ambiguous  term  is  used  in  a 
different  sense  from  that  originally  adopted, 
that  a  new  term  is  in  fact  illicitly  substituted. 
We  must  add,  therefore,  as  a  corollary  the 
following: 

Rule  VII.  THE  SENSE  OF  TERMS  TO  RE- 
MAIN UNALTERED. 

Every  verbal  expression,  ivJietJier  a  term  or 
proposition,  shall,  throughout  the  ratiocination, 
be  used  in  the  sense  originally  given  to  it. 

The  violation  of  this  rule  constitutes  what  is 
called  the  Fallacy  of  Equivocation,  which  is  to 


THE  RULES  OF  LOGIC  147 

be  regarded  as  a  species  of  Illicit  Substitution ; 
and  of  this  there  are  two  kinds:  the  first  con- 
sisting in  shifting  the  sense  of  an  ambiguous 
term,  which  is  called  the  Fallacy  of  Ambiguity  ; 
the  second,  in  shifting  the  meaning  of  what  is 
called  an  amphibolous  sentence,  which  is  a  sen- 
tence equivocal  by  reason  of  its  grammatical 
construction,  as,  e.  g.,  the  sentence,  "  The 
Duke  yet  lives  that  Henry  shall  depose"; 
which  may  mean  either  that  the  Duke  shall  de- 
pose Henry,  or  Henry  the  Duke.  If  construed 
in  the  former  sense,  the  subject  of  the  proposi- 
tion is,  "  The  Duke  that  shall  depose  Henry  "  ; 
for  which  under  the  latter  construction  is  sub- 
stituted, "  The  Duke  that  shall  be  deposed 
by  Henry."  This  is  called  the  Fallacy  of 
Amphibology,  or,  perhaps  better,  of  Amphiboly. 
But  these  fallacies  are  of  essentially  the  same 
nature,  and  will  be  classed  together  under  the 
one  head  of  Equivocation. 


PART  II 
THE  DOCTRINE  OF  FALLACIES 


CHAPTER  VIII 

DEFINITION   AND   CLASSIFICATION   OF   FAL- 
LACIES 

§  128.  DEFINITION  OF  FALLACIES. — A  fal- 
lacy may  be  defined  as  a  false  semblance  of 
valid  ratiocination ;  to  which  it  bears  the  same 
relation  as  hypocrisy,  conscious  or  unconscious, 
to  virtue.  Fallacy  is  therefore  a  species  of 
error,  whose  specific  difference  consists  in  its 
semblance  of  right  reasoning  and  its  conse- 
quent liability  to  be  mistaken  for  it.1  It  may 

1  Hobbes,  with  his  usual  acuteness,  thus  clearly  explains  the 
distinction  between  error  a.\\<\  fallacy  : 

"  When  we  reason  with  words  of  general  signification  (uni- 
•versalibus}  and  fall  upon  a  general  conclusion  (conclusionem 
universalum)  which  is  false,  though  it  be  commonly  called 
error,  it  is  indeed  an  absurdity  or  senseless  speech  (pratio 
insignificans)" — Lev.,  chap.  v.  According  to  this  view,  all 
fallacies  are  absurdities,  i.  e.,  they  necessarily  involve  either  a 
contradiction,  or  the  use  of  non-significant  or  senseless  words. 
149 


1 50  LOGIC 

consist  either  in  a  false  judgment  or  a  false  in- 
ference. But,  it  will  be  remembered,  the  terms 
judgment  and  inference  in  the  logical  sense  de- 
note, the  one  intuitive  judgment,  and  the 
other  illative  inference.  Hence,  when  we 
speak  of  a  false  judgment  or  inference,  we  do 
not  mean  a  real  judgment  or  inference  that  is 
untrue  (which  would  involve  a  contradiction 
of  terms),  but  —  as  when  we  speak  of  a  false 
prophet  — a  pretended  or  simulated  judgment 
or  inference  that  is  not  really  such. 

§  129.  CLASSIFICATION  OF  FALLACIES.— 
All  fallacies  must  consist  in  the  violation  of 
some  one  or  more  of  the  rules  of  Logic,  and 
hence  may  be  correspondingly  classified.  Such 
a  classification  has,  indeed,  already  been  sub- 
stantially effected  in  our  statement  of  the 
logical  rules;  where,  under  each  rule,  the  cor- 
responding fallacies  have  been  named.  It 
remains,  therefore,  only  to  arrange  them  in 
convenient  order,  which  is  done  in  the  table 
that  follows: 

Table  of  Fallacies 

§  130.  FALLACIES  OF  JUDGMENT. 

I.  Illicit  Premises. 

(1)  Fallacies  in  Definition. 

Nonsense  (or  Non-Significance). 
False  Definition. 

(2)  Illicit    Assumption    of    Premise    (Petitio 

Principii ). 


CLASSIFICATION   OF  FALLACIES          151 

II.   Mistaking  the  Issue,  or  Irrelevant  Conclusion 
(fgnoratio  Elenchi}. 

§  131.  FALLACIES  OF  INFERENCE,  OR  IL- 
LICIT SUBSTITUTIONS. 

I.   Illicit  Conversions  of  Propositions. 
II.  Illicit  Substitutions  of  Terms  ;  Scil. 

1 i )  Of  Vocal  Signs,  or  Vocables. 

Formal. 
Material. 

(2)  Of    Notions,    /.    e.,    of    Senses   of   Terms 

{Equivocation,     Homonymia    et    Amphi- 
bolia) . 

§  132.  OBSERVATIONS  ON  THE  FALLACIES. 
— Of  the  two  principal  kinds  of  fallacies  con- 
tained in  the  above  table,  the  first — excepting 
the  Fallacy  of  Irrelevant  Conclusion — consist  in 
the  illicit  assumption  of  the  propositions  to 
be  used  as  the  premises  of  ratiocination.  But 
false  or  nonsensical  propositions  do  not  of 
themselves  constitute  fallacies,  but  only  by 
reason  of  their  use  as  judgments;  for,  accord- 
ing to  our  definition,  a  fallacy  is  a  false  sem- 
blance of  ratiocination,  and  therefore  cannot 
exist  except  as  part  of  ratiocination.  Hence 
we  are  not  concerned  with  the  truth  or  falsity 
or  the  absurdity  of  any  proposition  that  may 
be  asserted  by  any  one,  unless  it  be  used  as  an 
independent  judgment  or  as  the  premise  of  an 


152  LOGIC 

argument,  in  which  case  its  pretensions  may 
be  examined,  and,  if  found  to  be  baseless,  it 
may  be  challenged  as  illicit. 

Where  such  an  assumed  premise  is  either 
non-significant  or  involves  a  false  definition,  it 
is  in  itself  a  fallacy,  and  therefore  entitled  to 
an  independent  rank  as  such.  But  such  fal- 
lacies are  innocuous  if  the  sense  of  the  terms 
be  preserved  unaltered  throughout  the  ratio- 
cination. For  all  conclusions  in  which  they 
are  involved  must  necessarily  be  without  sig- 
nificance, or,  in  other  words,  nonsensical,  and 
hence  unsusceptible  of  use.  But,  as  will  be 
seen  at  large  as  we  proceed,  the  conclusions 
from  such  premises,  being  in  themselves  un- 
susceptible of  use,  are  invariably  used  as 
equivalent  to  other  and  significant  proposi- 
tions, and  thus  inevitably  result  in  the  Fallacy 
of  Irrelevant  Conclusion,  or  Ignoratio  Elenclii, 
which  consists  in  substituting  for  the  conclu- 
sion another  proposition  (i.  e.,  the  true  thesis); 
and  which,  though  for  convenience  treated 
separately,  may  itself  always  be  resolved  into 
the  Fallacy  of  Illicit  Substitution,  i.  e.,  into  an 
illicit  conversion,  or  an  illicit  substitution  of  a 
term.  And  the  same  observation  is  true  gen- 
erally, though  not  universally,  of  illicit  assump- 
tions of  false  premises.  These,  if  regarded  as 
mere  hypotheses,  and  if  no  misuse  be  made  of 
the  conclusion,  are  not  illegitimate  ;  but,  it  will 


CLASSIFICATION  OF  FALLACIES          153 

be  seen,  a  conclusion  deduced  from  such  pre- 
mises almost  invariably  either  comes  in  conflict 
with  some  inconsistent  fact,  or  otherwise  fails 
to  be  sufficient  for  the  purposes  the  reasoner 
has  in  view;  and  thus,  almost  inevitably,  it  is 
treated  as  equivalent  to  some  other  proposi- 
tion, thus  again  presenting  a  case  of  Ignoratio 
Elenchi.  Hence — if,  as  we  conveniently  may, 
we  regard  all  assumed  propositions  as  mere 
hypotheses,  and  therefore  as  not  illegitimate, 
unless  an  ill  use  be  made  of  the  conclusion — 
all  illicit  assumptions  of  premises  must  neces- 
sarily result  in  an  Ignoratio  ElencJii  ;  which,  as 
we  have  observed,  must  necessarily  consist 
either  in  an  illicit  conversion  or  the  illicit 
substitution  of  a  term.  Hence,  as  all  valid 
ratiocination  consists  in  the  substitution  of 
equivalent  (§  78),  so  all  fallacy  must  consist  in 
the  substitution  of  non-equivalent  terms. 

Hence  the  simplest  and  most  scientific  classi- 
fication of  fallacies  would  be  to  regard  them 
all  as  species  of  illicit  substitution — that  is  to 
say,  as  cases,  either  of  illicit  conversion  of  pro- 
positions or  illicit  substitution  of  terms;  and 
that  we  have  adopted  a  different  mode  of  classi- 
fication is  due  simply  to  the  consideration  that 
we  may  thus  more  conveniently  exhibit  the 
different  sources  of  fallacy.  Hence,  as  we 
proceed,  it  will  be  found  that  the  several  fal- 
lacies all  have  a  tendency,  as  it  were,  to  run 


J54  LOGIC 

into  each  other;  which  mainly  results  from  the 
fact  that  they  are  all  in  their  essential  nature 
the  same,  differing  only  in  the  peculiar  sources 
in  which  they  originate;  though  partly  also 
from  the  fact  that,  in  general,  fallacious  argu- 
ments are  not  explicit,  and  the  fallacy  may 
vary  according  to  the  manner  in  which  we  may 
express  them. 

In  our  classification  of  the  fallacies  we  have 
distinguished  as  a  class  the  fallacy  of  "  Mis- 
taking the  Issue,  or  Irrelevant  Conclusion," 
thus  apparently  including  two  separate  fal- 
lacies. But  this  is  only  apparently  so.  For 
unless  there  be  some  fault  in  the  inference  — 
which  would  constitute  another  kind  of  fallacy 
— the  conclusion  and  the  premises  must  neces- 
sarily correspond,  and  we  may  therefore  regard 
either  the  illicit  assumption  or  the  illicit  con- 
clusion as  constituting  the  fallacy.  If  we  re- 
gard the  latter  as  the  fallacy,  it  necessarily 
resolves  itself  into  a  case  of  illicit  substitution. 
But,  for  convenience,  we  regard  it  as  relating 
to  the  premises,  and  thus  regarded,  it  consists 
in  the  illicit  assumption  of  one  proposition  in 
place  of  another — i.  e.,  of  the  actual  premise 
for  some  other  proposition  more  or  less  resem- 
bling it  which  is  admitted. 

In  concluding  these  introductory  observa- 
tions I  would  refer  the  student  to  what  is  said 
in  the  conclusion  of  the  Introduction,  and 


CLASSIFICATION  OF  FALLACIES          155 

which,    for  convenience   of  reference,   is  here 
repeated : 

"  In  our  treatment  of  the  subject,  the  several 
fallacies  will  be  illustrated  almost  exclusively 
by  examples  taken  from  current  theories  of 
Politics  and  Morality.  Our  examples  will 
therefore  consist,  not  of  mere  trivialities,  such 
as  are  so  commonly  used  in  works  on  Logic, 
but  of  fallacies  that,  in  perverting  moral  and 
political  theory  and  in  corrupting  practice, 
have  dominated,  and  still  continue  to  dominate, 
the  fortunes  of  the  world.  They  come  to  us, 
therefore,  as  veterans  in  the  army  of  what 
Hobbes  calls  the  '  Kingdom  of  Darkness,' 
crowned  with  the  laurels  of  victory  "  (§  13). 

Among  these  theories  there  are  two  fruitful, 
above  all  others,  in  examples  of  logical  fallacy 
—  namely,  the  modern  doctrine  of  Absolute 
Sovereignty,  and  the  Utilitarian  Theory  of 
Morality;  the  former  of  which  may  be  ex- 
pressed in  the  proposition  that  "  Sovereignty 
is,  in  its  essential  nature,  an  absolute  poiver, 
and,  as  such,  unsusceptible  either  of  limitation 
or  division";  the  latter,  in  the  proposition 
that  "  General  Utility  is  the  trite  and  only 
standard  of  justice  and  injustice,  and  of  right 
and  wrong  generally."  Most  of  our  examples 
will  be  taken  from  these  theories;  and  these, 
and  other  current  theories  used  for  the  same 
purpose,  will  be  found  not  only  to  serve  as  the 


1 56 


LOGIC 


most  effective  means  of  illustrating  the  nature 
of  the  several  fallacies  involved,  but  also  to 
enable  us  to  perceive  the  frequent  use  and 
formidable  influence  of  fallacy  upon  political 
and  moral  speculation,  and  to  realize  how  dis- 
astrously and  commonly  the  most  vital  affairs 
of  mankind  are  thus  affected. 


CHAPTER   IX 

NON-SIGNIFICANCE,    OR    NONSENSE — FALLACY 
OF 

§  133.  The  nature  of  this  fallacy  is  explained 
under  Rule  I.  of  the  Rules  of  Logic.  The  fal- 
lacy is  of  two  kinds;  namely,  (i)  where  a  term 
is  used  that  has  an  impossible  or  absurd  mean- 
ing or  no  meaning  at  all — which  constitutes  the 
Fallacy  of  Nonsense  in  the  narrower  sense  of 
the  term ;  and  (2)  where  an  ambiguous  term  is 
used  without  definition — which  is  called  the 
Fallacy  of  Confusion.  But,  logically,  the  two 
kinds  are  of  essentially  the  same  nature,  and 
hence  are  classed  together  under  the  general 
head  of  Non-significance  or  Nonsense.  For 
the  purpose  of  illustrating  their  nature,  they 
will,  however,  be  considered  separately. 

i .    The  Fallacy  of  Nonsense  ' 

§  134.  In  dealing  with  concrete  matters,  it 
is  difficult  to  use  nonsensical  speech  without 

1  According  to  Ilobbes  (cited  supra,  §  128,  n.),  all  fal- 
lacies, in  their  ultimate  analysis,  may  be  reduced  to  this  head. 

157 


158  LOGIC 

discovering  it;  and  hence  the  kind  of  nonsense 
to  which  the  term  is  colloquially  applied  is  gen- 
erally of  an  obvious  and  transparent  character. 
But  when  we  come  to  deal  with  abstract  terms, 
or  terms  of  second  intention,  such  as  are  con- 
stantly used  in  Morality,  Politics,  and  Meta- 
physics, the  case  is  quite  different.  For  here 
not  only  are  we  liable  constantly  to  use  non- 
sensical or  non-significant  terms,  but  it  often 
requires  the  most  searching  and  difficult  analy- 
sis to  discover  that  we  have  done  so.  Hence, 
the  nonsense  of  which  we  are  to  discourse  is 
something  very  different  from  the  nonsense  of 
colloquial  speech  ;  which  is  generally  so  obvious 
that  only  foolish  people  can  fall  into  it,  or,  at 
least,  persist  in  it.  It  is  a  kind  of  nonsense 
that  constantly  imposes  itself  upon  the  most 
eminent  statesmen,  jurists  and  philosophers, 
and  even  upon  the  most  acute  logicians.  To 
escape  it  altogether  a.  man  must  be  endowed 
with  more  than  mortal  sagacity,  and  hence  the 
fallacy  may  be  illustrated  by  examples  from 
the  writings  of  the  most  eminent  men. 

Examples 

§  135.  SOVEREIGNTY. — The  most  striking 
example  of  this  fallacy  is  presented  by  the 
modern  doctrine  of  Absolute  Sovereignty  (§ 
132),  a  doctrine  almost  universally  received  by 
modern  political  writers,  and  which  (with  an 


FALLACY  OF  NON-SIGNIFICANCE        159 

exception,  to  be  touched  upon  under  the  next 
head)  has  contributed  more  than  any  other 
cause  to  the  corruption  of  political  philosophy 
and  practice.  This  will  require  some  explana- 
tion. 

The  term  Sovereign,  in  its  original  and  proper 
sense,  denoted  merely  a  single  ruler  or  monarch, 
and  Sovereignty,  the  power  of  this  monarch. 
But  in  modern  times  the  application  of  these 
terms  has  been  much  extended,  and  the  latter 
term  is  now  used  in  many  different  ways;  of 
which  four  may  be  distinguished,  namely  :  (i) 
Personal  Sovereignty,  or  the  power  of  an  abso- 
lute monarch  —  otherwise  known  as  "the 
Divine  Right  of  Kings";  (2)  Corporate  Sover- 
eignty, or  the  Sovereignty  of  the  government, 
whether  monarchic,  aristocratic,  democratic, 
or  mixed;  (3)  Popular  Sovereignty,  or  the  Sov- 
ereignty of  the  state  or  people ;  and  (4)  The 
Sovereignty  of  Right  or  the  Lazu.1  To  which 
may  be  added  as  many  other  senses  as  abstrac- 
tions can  be  imagined  for  the  purpose — as,  e.  g. , 
the  Sovereignty  of  Reason,  or,  in  a  theocracy, 
the  Sovereignty  of  God.  All  these  different 

1  This  expression  originated  with  Aristotle  :  "  Moreover,  he 
who  bids  the  law  to  be  supreme,  makes  God  supreme  ;  but  he 
who  trusts  man  with  supreme  power  gives  it  to  a  wild  beast, 
for  such  his  appetites  often  make  him  ;  passion,  too,  influences 
those  who  are  in  power,  even  the  very  best  of  men  ;  for  which 
reason  the  law  is  intellect  free  from  passion." — Politics,  iii., 
xvi. 


l6o  LOGIC 

senses  of  the  term  are  inconsistent  with  each 
other;  and  all  except  the  first  (now  happily  ob- 
solete) are  —  in  their  direct  sense  —  without 
definite  signification,  or,  in  other  words,  non- 
sensical. For  the  government  or  state,  and 
likewise  right  or  law  and  reason,  are  purely 
imaginary  or  fictitious  persons,  existing  only 
in  contemplation  of  mind — /.  e. ,  they  are  quasi- 
persons  only;  and  the  power  of  such  fictitious 
or  imaginary  beings  must  be  as  imaginary  as 
themselves.  For  the  government  or  state  or  a 
corporation  cannot,  properly  speaking,  be  said 
to  have  rights,  or  will,  or  power,  or  conscience, 
or  other  human  attribute;  and  when,  other- 
wise than  as  a  mere  figure  of  speech,  we  speak 
of  such  <5w<7.$7-persons  as  having  such  attributes, 
we  talk  pure  nonsense.  And  so  with  reference 
to  the  sovereignty  of  God,  though  the  same 
observation  is  not  literally  true,  yet  practically, 
as  we  can  know  but  little  of  His  will,  or  the 
exertions  of  His  power,  the  term,  as  generally 
used,  carries  with  it  no  meaning. 

The  following  examples  are  in  effect  identical 
with  the  above : 

(i)  The  doctrine  of  Kant,  Rousseau,  and 
others,  that  the  will  of  the  government  or  the 
state  is  to  be  regarded  as  "  the  united  will  of 
the  people" ;  which  is  obviously  a  mere  fiction, 
and,  construed  literally,  not  only  false,  but 
impossible. 


FALLACY  OF  NON-SIGNIFICANCE        l6l 

(2)  The   proposition    of    Hobbes,   that   the 
effect  of  the  institution  of  government  was  to 
create  not  merely  "  a  consent  or  concord  "  of 
the  people,  but  "  a  real  unity  of  them  all  in  one 
and  the  same  person" 

(3)  The  equivalent  proposition  of  Bluntschli 
and  others,  that  the  state  is  an  "  organized  be- 
ing "  or  "organism,"  having  a  soul  and  a  body, 
a  conscience  and  active  powers,  and  also  a  will 
different  from  the  wills  of  the  individuals  com- 
posing it. 

(4)  And  finally  the  celebrated  theory  of  the 
Social    Compact    or     Contract,    which    served 
Hobbes,  Locke,  Rousseau,  and  others  as  the 
foundation  of  their  respective  reasonings;  and 
from  which,  as  a  premise,  their  several  essen- 
tially different  and  antagonistic  theories  are, 
with  equal  felicity,  deduced. 

§  136.  OF  LEGAL  FICTIONS. — These  are  all 
examples  of  what  lawyers  call  legal  fictions ; 
which  are  at  least  as  common  with  the  philoso- 
phers as  with  the  lawyers.1  In  all  of  them — 
except  the  last — the  government  or  state  is  re- 
garded as  a  body  politic  or  corporation ;  which 

1  The  difference  between  the  lawyers  and  the  philosophers 
in  this  respect  is  that  by  the  former  the  fiction  is  always  recog- 
nized as  such,  and  used  merely  as  a  convenient  mnemotechnic 
device.  It  is  also  used,  not  as  a  universal,  but  as  a  particular 
proposition — its  use  being  restricted  by  the  maxim,  "  In  fic- 
tione  juris  semper  tequilas."  But  the  use  of  it  by  philosophers 
is  often  the  reverse. 


I 62  LOGIC 

is  defined  as  a  fictitious  or  imaginary  person, 
existing  only  in  contemplation  of  mind, — i.e.,  as 
a  guasi-person, — and  the  definition  is,  in  fact, 
but  a  bold  metaphor.  Hence,  as  we  have  said, 
the  power  of  this  fictitious  or  imaginary  being  is 
as  imaginary  as  itself.  For  human  power  can 
exist  only  in  actual  human  beings;  and  though 
for  convenience  we  may  speak  of  the  power  of 
the  government  as  of  that  of  any  other  corpora- 
tion, yet  the  expression  is  always  to  be  under- 
stood as  really  denoting  the  concurrent  powers 
of  certain  individuals  in  the  government. 
Hence,  when  we  attribute  to  the  state  or  gov- 
ernment, or  any  other  corporation  or  fictitious 
entity,  will,  conscience,  soul,  body,  sex,  or  other 
human  faculty,  feeling,  or  quality,  we  speak 
figuratively,  and,  as  in  all  cases  of  figurative 
language,  if  literally,  absurdly.  The  examples 
cited  may  therefore  be  more  specifically  as- 
signed to  the  class  of  fallacies  called  by  the  old 
logicians  the  Fallacy  of  Figure  of  Speech  (Fal- 
lacia  Figures  Dictionis),  (infra,  §  203). 

With  regard  to  the  doctrine  of  a  social 
compact,  it  has  not  the  excuse  of  being  even 
figuratively  true.  Like  the  fiction  of  the  Eng- 
lish law  that  husband  and  wife  are  one,  it  is 
simply  an  undisguised,  recognized  absurdity, 
assumed  as  a  first  principle.  That  it  should 
ever  be  asserted  would,  were  it  not  for  experi- 
ence to  the  contrary,  be  simply  incredible. 


FALLACY  OF  NON-SIGNIFICANCE      163 

§  137.  THE  DARTMOUTH  COLLEGE  CASE.— 
A  similar  example  of  this  fallacy  is  presented 
by  the  decision  of  Chief  Justice  Marshall  in  the, 
Dartmouth  College  case  (4  Wheat.,  518),  where 
it  was  held  that  an  act  of  the  Legislature  re- 
organizing a  collegiate  corporation  was  in  con- 
flict with  the  provision  of  the  Constitution  of 
the  United  States  forbidding  enactment  by  a 
State  of  any  law  "  impairing  the  obligation  of 
contracts."  It  was  not  perceived  that  a  corpo- 
ration, being  a  fictitious  person,  is  not  capable 
of  having  any  rights,  except  as  representing 
real  persons,  and  that  its  so-called  rights  are  in 
fact  merely  the  rights  of  its  stockholders  or 
other  parties  interested  in  it.  But  in  eleemosy- 
nary corporations  there  are  no  private  parties 
interested,  and  hence  the  supposed  rights  of 
the  corporation  are  in  fact  those  of  the  State, 
and  consequently  subject  to  its  disposition. 
For  it  is  absurd  to  speak  of  rights  that  have  no 
real  owners;  and  to  such  rights  the  Constitu- 
tion— which  was  designed  to  protect  the  rights 
of  real  persons — can  have  no  application.  The 
decision  was  therefore  simply  a  case  of  the  Fal- 
lacy of  Nonsense,  of  the  kind  called  F.  Figures 
Dictionis. 

§  138.  OBSERVATIONS  ON  THE  FALLACY  OF 
NONSENSE. — It  may  be  observed  here  by  the 
reader,  who  is  somewhat  familiar  with  Logical 
Doctrine,  that  the  Fallacy  of  Nonsense  is  ap- 


1 64  LOGIC 

parently  a  new  kind  of  fallacy,  not  to  be  found 
in  the  books  ;  but  this  is  very  readily  explained. 
;For,  as  we  have  observed,  a  conclusion  involv- 
ing a  nonsensical  term,  being  itself  nonsensi- 
cal, can  in  its  proper  sense,  or  rather  nonsense, 
be  of  no  use  for  any  purpose,  and  hence  is 
always  used  as  equivalent  to  some  significant 
proposition,  and  thus  becomes  an  Ignoratio 
Elenchi.  Thus  the  doctrine  of  Absolute  Sov- 
ereignty, like  other  nonsensical  theories,  is  in 
itself  innocuous,  and  becomes  otherwise  only 
by  illicit  use.  There  can  be  no  harm  in  saying 
that  Leviathan,  the  creature  of  our  imagina- 
tion, is  vested  with  unlimited  power,  or  even 
to  say  with  Hobbes  that  he  is  a  "  mortal 
god,"  and  therefore  omnipotent.  For  his 
power,  if  left  to  himself,  is  no  more  formidable 
than  that  of  the  wooden  or  brazen  gods  of  the 
heathen.  But  as  in  the  latter  case  the  power 
of  the  god  is,  in  practice,  the  power  of  the 
priest,  so  the  imaginary  power  of  Leviathan  is 
but  a  word  used  to  cover  the  actual  power  of 
some  officer  or  officers  of  the  government;  and 
to  them  the  meaning  of  the  doctrine  is:  "  You 
must  not  resist  us."  Hence,  invariably,  a  non- 
sensical term  is  used  only  in  the  argument,  and 
the  conclusion  is  always  used  as  equivalent  to 
some  other  and  significant  proposition,  thus 
making  a  case  of  Irrelevant  Conclusion,  or 
Ignoratio  Elenchi;  under  which  head  it  is 


FALLACY  OF  NON-SIGNIFrCANCE        165 

commonly  treated.     Of  this  numerous  exam- 
ples will  be  given  in  the  sequel. 

2.    77^  Fallacy  of  Confusion 

§  139.  This  fallacy  is  recognized  in  the  books 
as  one  of  the  most  common  and  pernicious; 
and,  indeed,  it  is  a  commonplace  in  philosophy 
that  the  use  of  undefined  terms  is  one  of  the 
most  fruitful  sources  of  error.  The  nature  of 
the  fallacy  is  explained  under  Rule  I.  of  the 
Rules  of  Logic.  A  few  examples  will  be  suffi- 
cient to  illustrate  its  nature. 

Examples 

§  140.  UTILITARIANISM. — The  most  serious 
example  of  this  fallacy  is  presented  by  the 
theory  of  Utilitarianism  (§  132  ad  fin.),  which 
for  the  greater  part  of  a  century  has  exercised 
a  predominating  and  pernicious  influence  over 
English  thought.  The  theory,  briefly  stated, 
is  that  general  utility  is  the  paramount  and 
sole  standard  of  right  and  wrong  and  of  the 
just  and  unjust.  But  the  term  "  general  util- 
ity "  has  no  definite  meaning;  because  it  is  im- 
possible to  determine  from  it  who  are  the  people 
whose  utility  or  welfare  is  to  be  considered — 
whether  a  mere  majority  or  less,  or  two  thirds, 
or  three  fourths,  or  other  proportion ;  and 


1 66  LOGIC 

hence  the  proposition  must  be  regarded  as  non- 
significant or  nonsensical. 

§  141.  EDUCATION. — So  he  who  asserts  the 
benefit  of  education  is,  in  general,  talking  non- 
sense. For  education  is  but  the  development 
of  character, — mental,  moral,  and  physical,— 
and  may  be  either  good  or  bad.  For  there  is 
an  education  of  the  thief,  of  the  bully,  of  the 
tramp,  as  well  as  of  the  honest  man,  of  the 
hero,  of  the  efficient  man,  or  of  the  scholar, 
or  statesman,  or  philosopher.  And  so,  even 
among  legitimate  kinds  of  education,  there  is 
an  education  of  the  mechanic,  of  the  farmer,  of 
the  laborer,  of  the  lawyer,  of  the  doctor,  and 
many  other  kinds.  Consequently,  when  one 
asserts  the  benefit  of  education  generally, 
without  defining  the  term,  the  proposition  is 
nonsensical. 

§  142.  PROTECTION. — So  the  man  that  as- 
serts that  he  is  in  favor  of  the  protection  of 
American  industries  is,  in  general,  talking  pure 
nonsense.  For  there  are  many  kinds  of  pro- 
tection, as,  e.  g.,  (i)  The  prohibition  of  all 
foreign  imports  that  compete  with  our  own  in- 
dustries; (2)  the  equalization  of  the  cost  of 
production;  and  (3)  the  encouragement  of  in- 
fant industries;  and  until  we  are  told  which  of 
these  various  kinds  of  protection  is  intended 
the  proposition  conveys  no  definite  meaning. 

§  143.   EXPANSION. — So  when  an  American 


FALLACY  OF  NON-SIGNIFICANCE        167 

announces  himself  as  an  advocate  of  territorial 
expansion  he  is,  generally,  talking  nonsense; 
for  there  are  many  kinds  of  expansion,  among 
which  three  may  be  especially  distinguished, 
namely:  (i)  The  acquisition  of  contiguous 
homogeneous  territory  essential  to  the  safety 
of  the  government,  as,  e.  g.,  in  the  case  of  the 
purchase  of  Louisiana;  (2)  the  acquisition  of 
contiguous  and  homogeneous  territory  desir- 
able as  giving  room  for  the  expansion  of  popu- 
lation, but  not  essential  to  the  safety  of  the 
government,  as,  e.  g.,  the  acquisition  of  Cali- 
fornia, New  Mexico,  etc.  ;  and  (3)  the  acquisi- 
tion of  territory  far  removed  from  our  own,  of 
a  climate  unsuited  to  our  people,  and  inhabited 
by  an  alien  and  non-assimilable  race.  Such  a 
country  must  be  governed  by  despotic  power, 
and  its  acquisition  must  therefore  be  distin- 
guished from  other  kinds  of  expansion  by  the 
name  of  Imperialism. 


CHAPTER  X 

FALLACY    OF    FALSE    DEFINITION 

§  144.  The  nature  of  this  fallacy  is  explained 
under  Rule  II.  of  the  Rules  of  Logic.  As 
there  explained,  the  fallacy  is  of  two  kinds — 
consisting,  the  one  in  the  use  of  a  term  in  an 
improper  sense,  i.  e.,  in  a  sense  not  permitted 
by  the  usage  of  the  language  —  the  other,  in 
using  a  term  in  an  unreal  sense,  /.  e. ,  as  denot- 
ing a  notion  to  which  there  is  no  corresponding 
reality. 

The  former  kind  of  the  fallacy  is  not  admitted 
by  logicians  generally ;  for  it  is  an  unfortunate 
delusion  of  philosophers  that  they  are  at  liberty 
to  define  a  term  as  they  please.  But  whether 
this  claim  be  admitted  or  otherwise,  it  has  been 
the  source  of  infinite  error;  so  that  the  viola- 
tion of  the  rule,  if  not  regarded  as  a  fallacy, 
must  at  least  be  regarded  as  a  most  prolific 
mother  of  fallacy.  For  where  a  term  is  used 
in  a  novel  sense,  though  clearly  defined,  it  is 
hardly  within  the  power  of  the  human  intellect 
168 


FALLACY  OF  FALSE    DEFINITION       169 

to  emancipate  itself  from  the  influence  of  its 
usual  and  proper  signification.  Hence,  inevi- 
tably, the  use  of  improper  terms  will  result  in 
the  fallacy  of  Ignoratio  Elenchi. 

Examples 

§  145.  WHATELY'S  DEFINITION  OF  LOGIC. 
— Whately's  definition  of  Logic  as  "  the  science 
and  art  of  reasoning,"  and  of  Reasoning  as 
consisting  solely  in  syllogistic  inference,  pre- 
sents an  instructive  example  of  the  Fallacy  of 
False  Definition.  This  definition  excludes  from 
the  province  of  Logic  the  doctrine  of  Judgment, 
and,  as  involved  in  this,  the  doctrine  of  the 
Term,  and  also  that  of  the  fallacies  called  Non- 
logical  or  Material,  thus  mutilating  it  of  its 
most  vital  parts.  But  these  subjects  are  in- 
variably treated  of  by  the  logicians,  including 
himself,  arid — as  is  now  generally  admitted — 
belong  to  logical  doctrine ;  which  is  an  effective 
reductio  ad  absurduin  of  the  definition. 

§  146.  STEWART'S  DEFINITION  OF  REASON- 
ING.— From  the  same  false  definition  of  Logic, 
and  of  reasoning,  Dugald  Stewart  deduces  the 
paradoxical  conclusion  that  not  only  Logic,  but 
reasoning  itself,  is  but  of  little  utility;  which 
constitutes  a  still  more  effective  reductio  ad 
absurdum  of  the  falseness  of  the  definition.1 

1  "Of  the  different  elements  which  enter  into  the  composi- 
tion of  reason,  in  the  most  enlarged  acceptation  of  the  word, 


1 70  LOGIC 

§  147.  LOCKE'S  ATTACKS  ON  LOGIC.— 
Locke's  diatribes  against  Logic  had  their 
source  in  the  same  false  definition  of  Logic  as 
being  merely  the  doctrine  of  syllogism.  But, 
strangely  enough,  at  the  end  of  his  work  he 
gives  a  correct  definition  of  it;  which,  as  we 
have  seen,  he  takes  for  an  invention  of  his  own 
(§  no). 

§  148.  MILL'S  DEFINITION  or  LOGIC.— 
According  to  Mill's  definition,  "  Logic  is  not 
the  science  of  belief,  but  is  the  science  of  proof 
or  evidence,"  or,  as  otherwise  expressed,  "  the 
science  of  the  operations  of  the  understanding 
which  are  subservient  to  the  estimation  of  evi- 
dence." But  bearing  in  mind  the  essential 
difference  between  judgments  and  assumptions 
it  will  be  observed — if  we  leave  out  of  view 
axioms,  which  are  to  be  regarded  merely  as 
laws  or  conditions,  to  which  the  mind  operating 
intelligently  must  conform  —  that  the  former 
constitute  the  first  principles  of  all  demonstra- 
tive or  apodictic  reasoning,  and  therefore  ne- 
cessarily fall  within  the  province  of  Logic  ;  but, 
with  regard  to  assumptions,  that  Logic  is  not 
concerned  with  the  evidence  of  their  truth. 
But  the  term,  evidence,  in  its  proper  sense,  re- 
lates exclusively  to  assumptions  or  propositions 

the  power  of  carrying  on  long  processes  of  reasoning  or  deduc- 
tion is,  in  point  of  importance,  one  of  the  least." — Phil,  of 
the  Mind,  v.  ii,  p.  154. 


FALLACY  OF  FALSE  DEFINITION       l?l 

in  which  the  significative  relations  of  the  term 
are  not  intuitively  perceived;  and  hence,  with 
regard  to  such  propositions,  the  respective  pro- 
vinces of  Logic  and  of  the  other  sciences  are 
clearly  defined.  The  latter  deal  with  the  evi- 
dence of  the  propositions  assumed  ;  the  former, 
exclusively  with  inferences  from  them,  upon 
the  assumption  or  hypothesis  that  they  are  true. 
Hence  the  definition  of  Mill  precisely  reverses 
the  several  functions  of  Logic  and  of  the  other 
sciences  that  furnish  it  with  assumed  proposi- 
tions as  premises. 

§  149.  HAMILTON'S  DEFINITION  OF  LOGIC. 
—The  definition  of  Logic  as  "  the  science  of 
the  laws  or  forms  of  thought  "  may  be  cited 
as  another  example.  Logic  is  concerned,  not 
with  all  thought,  but  with  a  particular  kind  of 
thought  only — namely,  reasoning;  and  it  is 
concerned,  not  only  with  \\\z  forms,  but  with 
the  matter  of  reasoning.  The  definition  is 
therefore  at  once  too  wide  and  too  narrow;  it 
would  include,  e.g.,  rhetoric  and  grammar, 
and  would  exclude  the  best  part  of  Logic. 

§  150.  DEFINITION  OF  THE  LAW. — A  most 
striking  example  of  the  Fallacy  of  False  Defini- 
tion is  presented  by  the  definition  of  the  Law, 
invented  by  Blackstone  and  adopted  as  the  first 
principle  of  jurisprudence  by  Bentham  and 
Austin.  According  to  this  definition,  the  law 
is  merely  an  expression  of  the  will  of  the 


1^2  LOGIC 

government  —  an  obviously  false  and  illegiti- 
mate definition.  Yet  the  theory  of  Bentham 
and  Austin,  based  on  this  definition,  has  abso- 
lutely dominated  jurisprudence  in  England  and 
this  country  for  nearly  a  century;  and,  as  the 
result,  English  and  American  jurists  and  publi- 
cists have  lost  mental  touch  with  the  jurists  of 
other  countries  and  ages;  and  have  thus,  with 
reference  to  scientific  jurisprudence,  been  ren- 
dered incapable  of  dealing  with  this  great  and 
important  subject.  And  indeed  the  effect  of 
the  theory  on  the  practical  administration  of 
justice  has  been  scarcely  less  deleterious. 

§  151.  THE  THEORY  OF  PRIVATE  UTILITY. 
— Another  conspicuous  example  of  this  fallacy 
is  furnished  by  the  theory  of  individual  utility 
assumed  by  Hobbes,  Bentham,  and  Austin  as 
the  first  principle  of  Morality  and  Politics;  in 
which  self-interest  is  regarded  as  the  sole  pos- 
sible motive  of  human  conduct,  and  right  and 
wrong,  just  and  unjust,  and  good  and  evil  are 
defined  as  consisting  in  conformity  or  noncon- 
formity to  that  interest. 

§  152.  THE  GREATEST  GOOD  OF  THE 
GREATEST  NUMBER. —  Bentham  also  incon- 
sistently held  the  theory  that  "  the  greatest 
good  of  the  greatest  number"  is  the  true  stand- 
ard of  Morality  ;  which  must  either  be  regarded, 
like  the  theory  of  General  Utility,  as  simply 
nonsensical,  or  as  holding  that  the  standard  of 


FALLACY  OF  FALSE  DEFINITION'       173 

right  and  wrong  and  of  the  just  and  unjust  is 
the  good  of  the  majority.  An  execrable  doc- 
trine; for  it  cannot  be  asserted  that  the  life  or 
faculties  or  property  of  an  innocent  man  can 
be  converted  to  the  use  of  another  or  of  others, 
except  in  the  case  of  a  clearly  defined  right  in 
the  one  and  an  obligation  to  submit  to  it  in 
the  other. 

§  153.  MAINE'S  DEFINITION  OF  THE  LAW 
OF  NATURE. — Another  example  is  presented 
by  the  peculiar  and  curious  view  taken  by  Sir 
Henry  Maine  of  the  term  Jus  Nat ur ale  as 
used  by  the  Roman  lawyers,  and  its  equiva- 
lent, the  Law  of  Nature,  or  Natural  Law,  as 
used  by  modern  jurists  and  philosophers.  This 
notion,  he  erroneously  assumes,  had  its  origin 
in  the  supposed  state  of  nature  ;  which  doctrine, 
he  says,  the  Roman  jurisconsults  borrowed 
from  the  Greek  philosophers.  But  the  term 
Jus  Naturale,  or  Law  of  Nature,  is  one  of  the 
comparatively  small  class  of  terms  whose  mean- 
ing is  perfectly  definite  and  settled.  As  used  by 
jurists,  it  is  but  another  name  for  Natural  Jus- 
tice,1 or  Right  Reason  applied  to  the  jural 

1  Hobbes's  Lev.,  chap.  xxvi.  "It  is  not  used  among  them 
that  be  learned  in  the  laws  of  England  to  reason  what  thing 
is  commanded  or  prohibited  by  the  law  of  nature."  But, 
"  when  anything  is  grounded  on  the  law  of  nature,  they  say 
that  reason  will  that  such  a  thing  be  done  ;  and  if  it  be  pro- 
hibited by  the  law  of  nature,  they  say  it  is  against  reason  " 
(Doctor  and  Student,  chap.  v.).  "True  law  is  right  reason 


174 


LOGIC 


relations  of  men  ;  which,  as  universally  held  by 
them,  "  is  part  of  the  law  of  every  common- 
wealth in  the  world." 

conformable  to  nature"  (Cicero,  De  Rep.).  "  Right  reason  is 
what  we  call  law"  (id.,  De  Leg.).  "Natural  law  is  the 
rule  and  dictate  of  right  reason  "  (Taylor,  Elements  of  Civil 
Law).  ' '  The  law  is  intellect  free  from  passion  "  (Arist. ,  supra, 
§  135  n.). 


CHAPTER  XI 

ILLICIT    ASSUMPTION    OF    PREMISES  (PETITIO 
PRINCIPII} 

I.   Of  the  Nature  and  Several  Forms  of  this 
Fallacy 

§  1 54.  This  fallacy  may  occur  in  various  ways, 
and  it  would  therefore  be  an  "endless  task  to 
enumerate  or  classify  all  its  different  forms; 
nor  would  there  be  any  advantage  in  doing  so. 
There  are,  however,  several  forms  of  the  fallacy 
that,  on  account  of  their  frequent  occurrence 
and  their  powerful  influence  over  the  minds  of 
men,  demand  a  particular  consideration,  and 
to  these  our  attention  will  be  directed. 

§155  (i).  ILLICIT  GENERALIZATION. — The 
most  important  of  these,  which  may  be  called 
the  Fallacy  of  Illicit  Generalization,  consists  in 
the  use  of  a  universal  proposition  in  cases  where 
the  corresponding  particular  proposition  is 
alone  admissible.  This  fallacy  is  one  of  the 
most  common  and  formidable,  not  only  in 
popular  discourses,  but  in  more  pretentious 

12 

175 


1/6  LOGIC 

works  on  Politics  and  Morality;  for  almost  all 
the  wisdom  of  common  sense  is  embodied  in 
this  sort  of  propositions,  i.  e.,  particular  propo- 
sitions assumed  to  be  universal.  Such  propo- 
sitions may,  indeed,  be  used  with  profit  by 
men  of  sense  in  practical  affairs;  as,  in  general, 
when  a  question  presents  itself  it  is  easy  to 
perceive  whether  the  principle  should  be  ap- 
plied or  not;  or,  if  a  mistake  be  made,  it  is 
corrected  by  experience;  but  the  masses  of 
men  are  easily  misled  by  them.  Hence  they 
serve  well  for  rhetorical  purposes;  for  the 
hearer,  unless  of  a  critical  mind,  will  in  general 
accept  them  without  hesitation. 

Examples 

§  156.  COMMONPLACES. — The  most  impor- 
tant cases  of  this  fallacy  occur  in  the  use  of 
Commonplaces ;  by  which  is  meant,  opinions 
current  among  men  generally,  or  particular 
classes  of  men,  and  used  as  premises  for  reason- 
ing.1 These  are  commonly  founded  upon  some 
truth  which  they  purport  to  express,  and  to 
which  they  more  or  less  nearly  approximate; 

1  Hence  Bacon,  as  a  useful  rhetorical  device,  recommends 
the  preparation  of  tables  of  Commonplaces,  of  which  he  gives 
an  example  in  his  De  Augmentis ;  wherein  should  be  arranged, 
for  the  use  of  speakers  and  writers,  in  parallel  columns,  argu- 
ments pro  and  con,  or  theses  and  anti-theses,  on  all  questions 
of  general  interest. 


ILLICIT  ASSUMPTION  OF  PREMISES      1 77 

so  that  there  is  here,  as  "  in  all  things  evil,  a 
soul  of  truth."  But  they  are  hardly  ever  uni- 
versally true;  and  therefore  to  assume  them  as 
universals  is  illicit. 

§  157.  POPULAR  PROVERBS. — Of  these  com- 
monplaces, the  most  striking  examples  are 
furnished  by  popular  proverbs;  and  of  these, 
as  illustrating  precisely  the  nature  of  such 
maxims,  two  may  be  cited  that,  in  their  literal 
expression,  are  contradictory,  but,  as  maxims 
go,  may  both  be  said  to  be  true,  i.  e.,  they  are 
each  true  in  certain  cases,  but  neither  univer- 
sally. They  are  the  old  adages,  "  Never  put 
off  till  to-morrow  what  you  can  as  well  do  to- 
day "  and  "  Never  do  to-day  what  you  can  as 
well  put  off  till  to-morrow  " ;  the  first  of  which 
points  out  the  danger  of  procrastination,  the 
latter,  the  danger  of  committing  ourselves  be- 
fore necessity  requires.  It  may  be  readily  seen 
that,  according  to  circumstances,  either  of 
these  may  serve  as  a  useful  hint  for  conduct ; 
but,  in  using  it,  the  caution  of  the  nautical 
philosopher  is  to  be  observed,  that  "  the  bear- 
ing of  the  observation  lies  in  the  application 
of  it." 

§  158.  LEGAL  MAXIMS. —  Another  striking 
illustration  of  the  same  class  of  propositions  is 
furnished  by  what  are  called  the  maxims  of  the 
law ;  which,  in  general,  are  true  only  as  particu- 
lar propositions,  /.  e.,  only  in  particular  cases, 


178  LOGIC 

but  are  habitually  spoken  of  by  legal  writers  as 
"  first  principles,"  analogous  to  the  maxims  of 
science;  though  every  competent  lawyer  is 
familiar  with  the  fact  that  they  admit  of  numer- 
ous exceptions.  A  very  large  proportion  of  the 
so-called  principles  of  the  law,  and  of  the  rules 
founded  upon  them,  are  of  precisely  this  nature, 
z.  e.,  admit  of  exceptions,  and  are,  therefore, 
true  only  as  particular  propositions.  And  it  is 
also  a  fact  that  many  of  these  principles  and 
rules  are  opposed  by  others,  equally  approved, 
that  are  contradictory  to  them.  Hence,  if  we 
regard  bulk  only,  the  greater  part  of  the  law 
might  be  readily  and  advantageously  arranged 
in  a  table  of  contradictory  commonplaces, — i.  e., 
a  collection  of  theses  and  anti-theses, — as  sug- 
gested by  Bacon  in  the  De  A ugmentis;  wherein, 
under  each  topic,  one  column  should  represent 
the  one  side  and  the  other,  the  other,  of  the 
various  questions  that  may  arise  in  litigation. 
The  cases  might  also  be  arranged  in  the  same 
way. 

The  above  examples  are  all  cases  of  illicit 
generalization,  and  will  serve  to  show  how  wide- 
spread is  the  use  of  this  particular  form  of  illicit 
assumption  of  premise.  And,  it  may  be  added, 
such  is  the  lack  of  critical  acumen  in  the  gener- 
ality of  mankind,  that  the  fallacy  is  seldom 
detected,  and  consequently  it  constitutes  the 
most  powerful  of  rhetorical  devices. 


ILLICIT  ASSUMPTION  OF  PREMISES    1/9 

§  159(2).  OF  THE  FALLACY  OF  NON  CAUSA 
PRO  CAUSA. — Another  form  of  the  Fallacy  of 
Illicit  Assumption  of  Premise  is  presented  by 
the  fallacy  called  "  Non  causa  pro  causa"  ; 
which  is  also  called  the  fallacy  of  "  Post  hoc 
ergo propter  hoc."  It  consists  in  the  illicit  as- 
sumption that  an  event  preceding  another 
event  is  the  cause  of  the  latter,  as,  e.  g.,  that 
a  change  in  the  moon  is  the  cause  of  a  change  in 
the  weather ;  or  that  the  fact  of  thirteen  dining 
together  is  the  cause  of  any  accident  that  may 
happen  to  any  one  of  them ;  or  that  the  Dog 
Star  is  the  cause  of  heat.  This  is,  indeed,  one 
of  the  most  familiar  of  fallacies  in  political 
arguments,  where  it  is  common  to  argue  that 
the  condition  of  the  country,  whether  good  or 
bad,  is  caused  by  some  particular  policy,  as, 
e.  g.,  where  it  is  argued  alternately,  according 
to  vicissitudes  of  events,  by  the  one  party  that 
a  prosperous,  by  the  other  that  a  depressed, 
condition  of  affairs  is  caused  by  the  tariff  or 
other  political  measure.1 

1  It  will  be  observed  that  there  are  some  differences  of 
opinion  among  logicians  as  to  this  fallacy.  A  distinction  is 
made  between  what  is  called  the  causa  essendi  and  the  causa 
cognoscendi  ;  or  between  the  cause  of  an  event  and  the  cause 
of  our  knowing  it.  These  may  coincide,  as,  e.  g.,  when  from 
the  fact  of  its  raining  in  the  night  we  infer  that  the  ground 
will  be  wet  in  the  morning  ;  where  the  rain  is  both  the  causa 
essendi  and  the  causa  cognoscendi.  But,  when,  from  finding 
the  ground  wet  in  the  morning,  we  infer  that  it  rained  during 


l8o  LOGIC 

§  160(3).  ARGUING  IN  A  CIRCLE. — Another 
common  form  of  the  Fallacy  of  Illicit  Assump- 
tion is  presented  by  the  fallacy  called  arguing  in 
a  circle  ;  which  consists  in  assuming  for  a  prem- 
ise the  very  proposition  to  be  proved,  or  one 
obviously  equivalent  to  it,  or  one  that  is  form- 
ally involved  in  it.1  When  the  argument  does 
not  extend  beyond  a  single  syllogism  it  is 
called  a  Hysteron  Proteron  (the  First-last).2 

§  161  (4).  QUESTION-BEGGING  TERMS.— 
Another  very  common  and  very  dangerous 

the  night,  the  causa  cognoscendi  is  the  wet  ground,  from  which 
we  infer  the  causa  essendi,  i.  e.,  the  rain.  Logic  is,  however, 
concerned  with  the  causa  essendi  only  so  far  as  it  constitutes 
the  causa  cognoscendi  ;  and  hence  logically  the  distinction  may 
be  regarded  as  immaterial. 

1  This  occurs  most  frequently  in  the  use  of  synonyms,  and, 
as  observed  by  Whately,  is  peculiarly  favored  by  the  composite 
character  of  our  language.     It  can  occur  only  where  the  prop- 
osition assumed  is  so  obviously  equivalent  to  the  conclusion 
as  to  be  evidently  the  result  of  a  trick  or  inadvertence.     In 
general  the  premises  assumed  are  equivalent  to,  or  imply,  the 
conclusion  ;  and  the  conclusion  is  arrived  at  by  the  substitu- 
tion of  an  equivalent  term  ;  which  is  the  very  essence  of  ratio- 
cination.    Such    assumptions    are    not    only    admissible,    but 
inevitable.     Otherwise  all  syllogisms  would  be  fallacious, — as 
involving  a pctitio  principii  ;  and  inference,  inconceivable. 

2  The    following    is    a    striking    example    of    this    fallacy  : 
"  Since  every  unjust  act  is  inexpedient,  then  no  unjust  act  is 
expedient  ;   then  no  expedient  act  is  unjust  ;   then  every  expe- 
dient act  is  just."     This  has  been  given  as  a  valid  argument. 
But  the  premise  is  obviously  but  an  inference  from  the  conclu- 
sion, which  is  the  principle  of  the  reasoning  ;  and  for  it  the 
thesis  has  been  illicitly  substituted  as  the  premise. 


ILLICIT  ASSUMPTION  OF  PREMISES      l8l 

form  of  this  fallacy  is  that  of  using  question- 
begging  terms  (which  is  also  a  case  of  the  Fal- 
lacy of  False  Definition).  It  consists  either  in 
including  in  the  formal  definition  of  a  term 
some  unproved  assumption,  as  being  of  the  es- 
sence of  the  conception  denoted,  or  in  using 
the  term  without  formal  definition,  as  though 
such  assumption  were  included  in  its  meaning. 
By  this  method,  the  propositions  from  which 
our  conclusions  are  to  be  deduced,  instead  of 
being  proved  as  they  ought  to  be,  are  uncon- 
sciously imbibed  by  the  mind,  with  the  defini- 
tion, or  with  our  conception  of  the  term,  and 
the  conclusion  thus  in  effect  assumed.  The 
power  of  this  method  of  persuasion  is  well  un- 
derstood by  many,  and  unscrupulously  used — 
as,  for  example,  by  Hobbes  and  other  support- 
ers of  governmental  absolutism  ;  who  realize 
the  truth  of  Rousseau's  observation  that  "  the 
strongest  is  not  strong  enough  to  continue  al- 
ways master,  unless  he  transforms  his  power 
into  a  right,  and  obedience  into  a  duty."  But 
with  the  mass  of  writers  the  fallacious  process, 
though  none  the  less  efficacious,  is  entirely 
unconscious.  A  notable  example  of  this  fallacy 
is  usually  given  by  political  writers  in  their 
definitions  of  "  the  State";  which  is  simply 
an  independent  society  of  men,"  but  is 
usually  defined  so  as  to  include  in  its  essence 
absolute  power,  or  some  other  theory  of  the 


I 82  LOGIC 

writer.     Any  recent  work  on  Politics  will  serve 
to  illustrate  the  fallacy. 

2.   Of  tlie  Tests  of  Illicit  Assumption 

§  162.  ENUMERATION  OF  THE  TESTS.— 
There  are  numerous  tests  by  which  the  legiti- 
macy of  assumed  premises  may  be  determined, 
of  which  the  most  important  and  familiar  are: 

(1)  the    ''Instance,''1   or  "  Extreme   Case"; 

(2)  the  "  Burden  of  Proof,"  or  Onus  Probandi ; 
and  (3)  the  Reductio  ad  Absurdum.     These  will 
next  be  considered. 

§  163.  THE  INSTANCE,  OR  EXTREME  CASE. 
— This  test  applies  most  appropriately  to  the 
Fallacy  of  Illicit  Generalization,  and  is  most 
efficacious  in  its  operation  ;  though,  as  is  ob- 
served by  De  Morgan,  it  is  commonly  regarded 
as  not  only  inadmissible,  but  impertinent.  It 
consists  simply  in  adducing  an  exception  to  the 
proposition  assumed.  The  subject  is  admi- 
rably treated  by  the  author  cited.2 

§  164.  THE  ONUS  PROBANDI. — An  ex- 
tremely effective  means  of  testing  the  truth  of 

1  The  term  ' '  instance  "  is  commonly  used  as  synonymous  with 
''  example,"  but  it  is  said  by  De  Morgan  that  by  the  mediaeval 
logicians  it  was  always  used  to  denote  an  inconsistent  example, 
or,  in  other  words,  to  denote  what  we  would  call  an  instance 
to  the  contrary, — an  expression  that  would  have  been  regarded 
by  them  as  tautological. 

2  "The  application  of  the  extreme  case  is  very  often  the 
only  test  by  which  an  ambiguous  assumption  can  be  dealt 


ILLICIT  ASSUMPTION   OF  PREMISES      183 

a  proposition,  and  of  thus  exposing  an  Illicit 
Assumption,  is  often  afforded  by  considering 
what  is  the  presumption  in  the  case ;  or,  con- 
trariwise, on  which  side  of  the  question  lies  the 
burden  of  proof ,  or  onus  probandi.  In  general, 
this  is  on  the  party  affirming  the  proposition, 
and,  in  the  absence  of  other  presumptions,  we 
are  always  entitled  to  demand  his  proofs.  This 
simple  test  will  be  sufficient  to  dispose  of  all 
propositions  for  which  proofs  cannot  be  found, 
but  which  have  been  inadvertently  assumed ; 
and  this  test  we  should  always  apply  to  our 
own  reasoning,  remembering  that  "  Slowness 
of  belief  and  distrust  are  the  very  sinews  of 
wisdom."  But  in  certain  cases,  and  especially 
in  Moral  and  Political  Science,  the  test  will 
often  have  a  conclusive  efficacy.  For  in 
Morality,  Public  and  Private,  or  in  Jurispru- 
dence or  Right,  the  questions  presented  are 
generally  questions,  not  of  fact,  but  of  right 
and  wrong ;  and  among  these  there  are  certain 
fundamental  principles,  as,  e.g.,  touching  the 
right  of  personal  liberty  or  security  or  self- 
ownership,  with  reference  to  which  the  pre- 
sumption is  clearly  defined,  and  its  contradictory 
obviously  absurd.  Of  this  kind  is  the  general 
presumption  in  favor  of  liberty;  which,  of 

with  ;  no  wonder  that  the  assumer  should  dread  and  protest 
against  a  process  which  is  as  powerful  as  the  sign  of  the  cross 
was  once  believed  to  be  against  evil  spirits." — Formal  Logic. 


1 84  LOGIC 

itself,  is  sufficient  to  dispose  of  numerous  and 
important  political  theories  that,  from  a  neglect 
to  consider  the  onus  probandi,  have  been  care- 
lessly or  dishonestly  assumed. 

§  165.  OF  THE  REDUCTIO  AD  ABSURDUM. 
— This  consists  in  reasoning  from  the  conclu- 
sion deduced  from  the  premises  assumed  to 
some  absurd,  or  admittedly  untrue,  conclusion  ; 
and  this  method  of  refutation  will  apply  not 
only  to  the  fallacy  of  illicit  generalization,  but 
to  all  forms  of  petitio  principii  whatever.  It 
is,  indeed,  one  of  the  most  efficacious  means 
that  Logic  has  at  its  command  for  the  detection 
of  fallacy,  and  will  therefore  repay  an  attentive 
consideration. 

Strictly  speaking,  the  phrase  would  seem  to 
indicate  that  it  applies  only  to  the  establish- 
ment of  the  contradictory  of  the  proposition 
under  consideration  ';  but  the  method  has,  in 
fact,  a  much  wider  application,  and  the  term, 
in  common  use,  a  corresponding  extension. 
For  it  is  the  essential  characteristic  of  all  true 

1  In  the  narrower  sense,  the  term  reductio  ad  absurdiim  is 
equivalent  to  the  reductio  ad  impossibile ;  of  which  examples 
are  given  supra  (§  96,  n.).  But  more  generally  it  is  used 
as  including  all  cases  where,  from  the  conclusion  of  an 
argument,  the  contradictory  of  some  admitted  proposition — 
or,  in  other  words,  a  conclusion  contrary  to  the  hypothesis 
— can  be  deduced.  Hence  it  is  called  by  Aristotle  the  "Argu- 
ment from  Hypothesis."  (Mansel's  Aldrich,  App.,  note  I, 
p.  228.) 


ILLICIT  ASSUMPTION  OF  PREMISES      18$ 

propositions  that  they  will  be  consistent  with 
each  other;  and  it  is  an  almost  equally  univer- 
sal characteristic  of  untrue  propositions  that 
they  will  be  inconsistent  with  other  proposi- 
tions known  to  be  true. 

This  is  particularly  the  case  in  all  the 
different  branches  of  the  Science  of  Human 
Nature ;  all  of  whose  parts  and  particular  prin- 
ciples are  so  connected  by  numerous  relations 
that  it  is  almost  impossible  to  assert  an  untrue 
principle  without  coming  in  conflict  with  others 
that  are  self-evident,  or  readily  demonstrable, 
and  which  have  thus  come  to  be  universally 
admitted.  Hence  it  may  be  said  that  in 
Morality  or  Politics  we  may  set  out  from  al- 
most any  principles,  provided  we  hold  them 
with  indifference  and  are  capable  of  abandon- 
ing them  when  shown  to  be  inconsistent  with 
settled  principles  and  known  facts.  From 
which  it  may  be  inferred  that  the  reductio  ad 
absurdum  in  fact  constitutes  not  only  an  effi- 
cient, but  almost  an  all-sufficient,  instrument 
for  the  detection  of  fallacy  in  Moral  and  Politi- 
cal Science. 

General  Examples 

§  166.  LOCKE'S  THEORY  OF  SIMPLE  IDEAS. 
— A  most  instructive  example  of  Illicit  As- 
sumption of  Premise  occurs  in  the  fundamental 
assumption  of  Locke's  theory  of  knowledge; 


1 86  LOGIC 

which  is,  that  the  original  notions  received  in 
the  mind  from  sensible  objects  are  notions  of 
the  qualities  of  substances,  such  as  color,  hard- 
ness, etc.,  which  he  calls  simple  ideas ;  and  out 
of  which,  he  holds,  all  our  notions  are  com- 
pounded. But  on  reflection  it  will  be  perceived 
that  the  original  or  primordial  notions  of  the 
mind  are  the  composite  notions  of  substances 
or  things ;  and  what  Locke  calls  "  simple  no- 
tions "  are  the  result  of  subsequent  analysis. 

§  167.  THE  OBLIGATION  OF  CONTRACTS.— 
It  is  one  of  the  so-called  maxims  of  the  law 
that  contracts  are  obligatory  and  ought  to  be 
enforced  (Pacta  quczlibet  servanda  sunf);  and 
this  is  commonly  assumed  as  a  universal  prop- 
osition, as,  e.  g.,  by  Bentham  and  Spencer  in 
the  examples  given  below  (§§  180,  181).  But 
there  are  innumerable  cases  in  which  it  is 
obviously  not  right  that  contracts  should  be 
enforced,  and  in  which,  in  fact,  the  law  does 
not  enforce  them  ;  which  is  an  effectual  refuta- 
tion of  the  principle.  The  true  principle  is 
that  in  case  of  breach  of  contract  the  injured 
party  is  entitled  to  compensation — as  in  the 
case  of  torts — for  the  detriment  suffered  by 
him  by  the  acts  of  the  wrongdoer  (i.  e.,  by  the 
making  of  the  contract  and  its  breach). 

§  168.  FALSE  ASSUMPTION  OF  FACT. — This 
includes  innumerable  cases,  which  it  would  be 
impossible  to  classify.  One  of  the  most  in- 


ILLICIT  ASSUMPTION  OF  PREMISES   1 87 

teresting  is  furnished  by  Tacitus  in  his  account 
of  the  mutiny  of  the  Pannonian  legions  on  the 
accession  of  Tiberius, — in  the  address  of  the 
soldier,  Vibulenus,  to  the  general,  Bloesus. 
His  brother,  he  said,  coming  as  a  delegate 
from  the  German  army,  had  been  butchered 
by  the  commands  of  Bloesus.  "  Answer, 
Blcesus,"  he  said;  "  where  hast  thou  thrown 
away  his  corpse  ?  "  By  which,  says  Tacitus, 
he  raised  such  a  spirit  of  frenzy  and  ven- 
geance that  had  it  not  been  quickly  manifested 
that  there  was  no  corpse  to  be  found 
and  that  Vibulenus  never  had  any  brother, 
they  had  gone  nigh  to  sacrifice  the  general." 
The  example,  so  far  as  Vibulenus  is  concerned, 
was  simply  a  lie,  but,  in  the  soldiers,  a  fallacy 
that  would  have  been  readily  refuted  by  apply- 
ing the  test  of  the  onus probandi. 


CHAPTER  XII 

MISTAKING    THE    ISSUE,    AND    IRRELEVANT 
CONCLUSION   (IGNORATIO  ELENCHI) 

§  169.  The  nature  of  this  fallacy,  which  is 
explained  under  Rule  IV.  of  the  Rules  of 
Logic,  is  precisely  expressed  by  the  first  of 
the  names  we  have  given  it,  which  is  a  techni- 
cal term  taken  from  the  law.  This  differs  from 
the  equally  appropriate  term  Irrelevant  Conclu- 
sion only  in  this,  that  the  former  has  regard  to 
the  origin,  the  latter  to  the  outcome  of  the  fal- 
lacy. Or,  in  other  words,  when  we  regard  the 
beginning  of  the  fallacy,  we  call  it  Mistaking 
the  Issue;  when  the  end,  Irrelevant  Conclu- 
sion; and,  in  either  case,  Ignoratio  ElencJii. 
The  two  names,  i.  e.,  Mistaking  the  Issue  and 
Irrelevant  Conclusion,  present,  therefore,  two 
different  aspects  of  the  same  fallacy,  under 
each  of  which  it  will  be  convenient  to  consider 
it. 

§  170.  MISTAKING  THE  ISSUE. — This,  as  is 
well  appreciated  by  the  lawyers,  is  one  of  the 
most  formidable  and  most  common  of  all  fal- 
188 


MISTAKING  THE   ISSUE  189 

lacies.  For  the  most  fruitful  of  all  sources  of 
fallacy  is  bias  or  logical  dishonesty,  of  which  the 
expedient  of  mistaking  or  misstating  the  ques- 
tion at  issue  is  one  of  the  most  obvious  and 
most  potent  instrumentalities.  And  as  logical 
honesty  is,  in  fact,  one  of  the  rarest  of  intel- 
lectual virtues,  it  can  be  readily  understood 
that  the  fallacy  must  be  common. 

§  171.  FALLACY  OF  SEVERAL  QUESTIONS 
OR  ISSUES. — One  form  of  this  fallacy  may  be 
identified  with  the  technical  Fallacia  plurium 
interrogationum  (§  197),  which  consists  in  mix- 
ing in  one  several  questions  or  issues.  As 
defined  by  Aristotle,  it  results  "  from  making 
two  questions  one,  when  it  escapes  notice  that 
there  are  many,  and  one  answer  is  given,  as  if 
there  was  one  question  only." 

The  following  examples  are  taken  from  a 
recent  work : 

Did  you  steal  anything  when  you  broke 
into  my  house  last  night  ?  '  '  Are  you  the  only 
rogue  in  your  family  ? '  '  Have  you  quit  drink- 
ing ?  '  '  Have  you  cast  your  horns  ? '  (Hence 
sometimes  called  Cornutus.}" — (Davis,  Theory 
of  Thought,  294.) 

The  fallacy  is  readily  solved  by  separating 
the  compound  question  into  its  several  compo- 
nents,— as,  e. g. ,  in  the  following:  Menedemus, 
Alexino  rogante,  Numquid,  pair  em  verberare 
desiisset  ?  inquit,  Nee  verberavi,  ncc  desii ;  or, 


190  LOGIC 

as  in  the  answers  of  the  two  thieves  to  the 
question:  "  Did  you  steal  the  sheep  you  have 
in  your  possession  ?";  to  which  the  one  an- 
swered, "  He  did  n't  steal  the  sheep";  the 
other,  that  "  He  did  n't  have  it." 

§  172.  It  is  added  by  the  author,  "  All  this 
seems  quite  frivolous."  And  another,  gener- 
ally accurate,  logician  says:  "  The  so-called 
'  Fallacia  plurium  interrogatiomim  '  has  not 
been  noticed  in  the  text,  because  it  is  a  rhe- 
torical artifice  rather  than  a  logical  fallacy." 
(Fowler,  Deductive  Logic,  150.)  But  it  cannot 
be  doubted  that  the  fallacy,  as  described  by 
Aristotle,  consists  simply  in  mixing  several 
questions  or  issues  in  one,  and  therefore  comes 
under  the  head  of  mistaking'  the  issue;  or  that 
it  is  at  once  a  very  common  and  a  very  for- 
midable fallacy.  And  especially,  it  is  to  be 
observed,  it  is  the  hard  fortune  of  the  citizen, 
in  all  ages  and  countries,  that,  in  general, 
whether  by  accident  or  design,  no  question  in 
practical  politics  is  presented  to  him  that  does 
not  involve  this  fallacy. 

Thus,  in  American  politics,  for  some  time 
after  the  war,  several  questions  (plures  intcr- 
rogationes)  were  presented  at  each  federal 
election,  namely:  (i)  as  to  the  expediency  of 
the  protective  policy;  (2)  as  to  that  of  the  re- 
construction policy;  (3)  as  to  that  of  the  con- 
traction of  the  currency;  and  thus  practically 


MISTAKING  THE  ISSUE  19! 

the  questions  presented  to  each  voter  were: 
"  Are  you  in  favor  of  all  these  policies  ? "  or 
"  Are  you  against  them  all  ?"  So  in  the  last 
election,  the  issues  presented  were  equally 
numerous  —  namely  :  (i)  as  to  the  policy  of 
protection  ;  (2)  as  to  the  relative  advantages  of 
the  single  gold  or  a  bimetallic  standard ;  and 
(3)  —  assuming  the  desirability  of  bimetallism 
— as  to  the  practicability  of  adopting  it  in  this 
country  alone,  without  the  concurrence  of 
other  nations. 

In  the  case  put,  and  in  fact  in  almost  all 
political  contests,  each  question  involved  is  dis- 
cussed separately,  and  the  conclusion  pro- 
fessedly drawn  is  simply  the  affirmative  or  the 
negative  of  the  particular  question,  as  the  case 
may  be;  but  the  conclusion  intended  is,  not 
the  affirmative  or  negative  of  the  particular 
question,  but  that  of  all  of  them  taken  to- 
gether—  thus  presenting  a  case  of  irrelevant 
conclusion. 

Hence,  generally,  in  political  contests  the 
actual  issue  presented  is  simply  as  to  the  as- 
cendancy of  one  of  two  parties;  while  the 
voters  are  persuaded,  or  persuade  themselves, 
that  they  are  deciding  some  other  issue.  Hence 
it  results  —  as  a  general  though  not  as  a  uni- 
versal proposition  —  that  politics  becomes  a 
mere  struggle  for  political  supremacy. 

§  173.  IRRELEVANT  CONCLUSION.— All  fal- 


IQ2  LOGIC 

lacies  of  judgment  must,  as  we  have  observed, 
take  the  form  of  irrelevant  conclusion  (§  132); 
which,  in  turn,  becomes  a  fallacy  only  when 
used  as  an  equivalent  to  some  other  proposi- 
tion. Hence  the  examples  of  fallacy  already 
given,  and  many  of  those  to  be  given  hereafter, 
will  equally  serve  our  present  occasion. 

Examples 

§  174.  THE  DOCTRINE  OF  ABSOLUTE  SOV- 
EREIGNTY.— The  use  made  of  this  doctrine  by 
its  advocates  presents  a  conspicuous  example 
of  this  fallacy.  The  doctrine,  like  all  other 
nonsensical  theories,  is  in  itself  innocuous,  and 
becomes  otherwise  only  by  illicit  use.  But  it 
is  invariably  used  in  some  different  and  signifi- 
cant sense,  as,  e.  g.,  Rousseau's  theory  of  the 
"  Sovereignty  of  the  People,"  which  gave  rise 
to  the  various  political  doctrines  rife  in  the 
French  Revolution,  and  to  which  historians 
have  ascribed  the  terrible  scenes  of  the  Reign 
of  Terror  ;  from  which  they  draw  the  infer- 
ence that  it  is  dangerous  to  apply  Logic  to 
practical  politics.  But  this  also  is  a  case  of 
Irrelevant  Conclusion.  For  the  conclusion 
should  be  only  that  Fallacy  is  dangerous,  i.  e., 
not  Logic,  but  the  want  of  Logic. 

§  175.  SOVEREIGNTY  OF  THE  LAW. — Of  the 
various  forms  of  the  doctrine  of  Sovereignty, 
that  of  the  Sovereignty  of  Right,  or  the  Law,— 


MISTAKING  THE  ISSUE  193 

as  it  metaphorically  expresses  a  doctrine  at 
once  true  and  fundamentally  important, — might 
seem  to  be  unobjectionable  were  it  not  that,  in 
the  direct  effect  of  its  language,  it  is  merely 
nonsensical,  and  therefore  liable  to  be  used  as 
equivalent  to  some  other  form  of  the  doctrine, 
as,  e.  g.,  in  the  use  made  of  it  by  Von  Hoist  in 
his  Constitutional  History  of  the  United  States  ; 
where  his  expressed  conclusion  is  that  "  Sover- 
eignty is  One  and  Indivisible — the  Sovereignty 
of  the  Law"  '  But  his  real  doctrine — to  the 
establishment  of  which  all  his  arguments  are 
marshalled — is  that  sovereignty  is  indivisible, 
and  therefore  vested  exclusively,  not  in  the 
law,  but  in  the  Federal  Government,  and  not 
to  any  extent  in  the  States. 

§  176.  AUSTIN'S  USE  OF  THE  DOCTRINE  OF 
SOVEREIGNTY. — An  example  of  this  fallacy  is 
furnished  by  Austin  and  his  followers  in  the 
use  made  by  them  of  their  conclusion,  that 
' '  Sovereign  poiver  is  incapable  of  legal  limita- 
tion "/  which,  accepting  his  definition  of  the  law 
as  being  merely  an  expression  of  the  will  of  the 
sovereign,  is  quite  true,  and  altogether  inno- 
cent; for  obviously  one's  power  cannot  be  said 

1  This — though,  if  the  sense  of  the  term  be  observed,  a 
harmless  proposition — is  not  a  very  consistent  one  ;  for,  as  in 
the  United  States,  each  State,  as  well  as  the  Federal  Govern- 
ment, has  its  own  independent  system  of  law,  it  would  seem 
to  follow  that  there  are  several  sovereignties. 
13 


194  LOGIC 

to  be  limited  by  his  own  will ;  but  the  proposi- 
tion is  habitually  used  in  the  ordinary  sense  of 
the  terms. 

§  177.  USE  OF  THE  DOCTRINE  BY  HOBBES. 
— Another  example,  precisely  similar,  is  fur- 
nished by  Hobbes,  who  logically  deduces  from 
his  premises  the  conclusion  that  "  the  right  or 
just  power  "  of  the  sovereign  over  the  life  and 
fortunes  of  the  subject  is  unlimited;  and  the 
corresponding  duty  of  the  subject,  absolute; 
which,  according  to  his  definition  of  the  terms, 
right,  justice,  and  duty,  means  simply  that  the 
so-called  right  of  the  sovereign  is  an  unbridled 
or  lawless  power,  to  which  prudence  demands 
of  the  subject  that  he  should  submit  for  fear  of 
worse  consequences.  The  conclusion,  in  the 
sense  of  the  terms  defined,  is,  therefore,  quite 
true;  but  it  is  habitually  used  by  him  and  by 
modern  English  jurists  as  though  the  terms, 
right,  justice,  and  duty  were  defined  in  their 
ordinary  and  proper  sense. 

§  178.  BENTHAM'S  MISUSE  OF  THE  THEORY 
OF  PRIVATE  UTILITY. — But  the  most  flagrant 
example  of  this  fallacy  is  that  of  Bentham,  who, 
having  established,  or  professed  to  have  estab- 
lished, the  doctrine  of  Private  Utility,  or  Utility 
to  the  Individual, — which  asserts  that  the  sole 
possible  motive  of  human  conduct  and  the 
only  standard  of  right  and  wrong  is  self-inter- 
est,— afterwards  assumes  as  equivalent  to  it  the 


MISTAKING  THE   ISSUE  195 

principle  of  General  Utility,  and  systematically 
uses  the  latter  as  the  premise  established. 

§  179.  MISUSE  OF  THE  THEORY  OF  GEN- 
ERAL UTILITY.—  This  theory,  in  the  use 
habitually  made  of  it  by  Bentham  and  by 
utilitarians  generally,  also  presents  a  most  in- 
structive example  of  this  fallacy.  The  theory, 
being  non-significant,  is  in  itself  innocuous ;  but 
it  is  commonly  used  as  equivalent  to  the  pro- 
position that  the  interest  of  the  majority  is  the 
sole  test  of  right,  or,  as  expressed  by  Bentham, 

as  equivalent  to  the  sacred  truth  that  the 
greatest  good  of  the  greatest  number  is  the 
foundation  of  morals  and  legislation."  Thus 
we  have  the  apparently  innocuous  principle  of 
General  Utility  converted  into  the  execrable 
maxim  that  the  good  of  the  majority  is  alone 
to  be  consulted. 

§  180.  BENTHAM'S  DEFENCE  OF  USURY.— 
Bentham's  celebrated  defence  of  usury  has 
been  commonly  regarded  ever  since  its  publica- 
tion as  finally  settling  the  question  involved  ; 
but  in  fact  it  presents  a  striking  example  of  the 
fallacy  of  Ignoratio  ElencJii. 

His  thesis,  as  proposed,  is  to  establish  "  the 
liberty  of  making  one 's  own  terms  in  money  bar- 
gains "/  and  his  conclusion,  which  is  entirely 
legitimate,  is  that  no  man,  not  under  disability, 

ought  to  be  hindered,  with  a  viciu  to  his  own 
advantage,  from  making  such  bargains  in  the 


196  LOGIC 

way  of  obtaining  money  as  he  sees  fit."  But 
obviously  this  is  to  mistake  the  issue ;  for  the 
question  is,  not  whether  one  should  have  the 
liberty  of  making  usurious  contracts,  but 
whether  he  should  be  compelled  to  perform 
them  (§  167),  and  hence  his  conclusion  is 
obviously  irrelevant.  He  fails,  therefore 
(though  the  world  has  thought  differently),  to 
establish  his  proposition.1 

§  181.  SPENCER'S  ARGUMENT. — Spencer's 
argument — in  Social  Statics  and  Justice — for 
liberty  of  contract  is  also  an  example  of  the 
same  fallacy.  His  first  principle  is  his  well- 
known  law  of  equal  liberty,  namely,  "  that 
every  man  is  free  to  do  that  which  he  ivills,  pro- 
vided that  he  infringes  not  the  equal  freedom  of 
any  other  man."  From  this  principle  he  de- 
duces, with  admirable  logic,  the  several  per- 
sonal rights  that  may  be  summed  up  in  the 
general  right  of  self-ownership,  and  also  the 
right  of  property,  and,  as  a  corollary  to  the  last, 
the  right  of  free  exchange,  and  from  that  (illog- 
ically,  §  189)  the  right  of  free  contract ;  but 
he  illicitly  assumes,  with  Bentham,  that  the 

1  In  these  observations  it  will  be  understood  we  are  con- 
sidering, not  the  moral  or  political  question  as  to  the  propriety 
of  enforcing  contracts  for  the  payment  of  interest  (on  which 
we  have  nothing  to  say),  but  simply  the  logical  question  as  to 
the  validity  of  an  argument  in  favor  of  usury  that  has  served 
to  convince  mankind  of  its  righteousness,  and  that  is  univers- 
ally regarded  by  an  unlogical  world  as  conclusive, 


MISTAKING  THE  ISSUE  197 

question  is  one  touching  the  liberty  of  contract, 
and  not  as  to  the  righteousness  of  coercing  the 
parties  (§  167),  which  was  his  thesis.  Hence 
his  conclusion  is  essentially  distinct  from  the 
real  conclusion  intended,  which  is,  that  men 
should  be  compelled  to  perform  contracts. 

§  182.  BERKELEY'S  THEORY  AS  TO  THE 
NON-EXISTENCE  OF  MATTER. — This  furnishes 
another  example.  His  argument  is  that,  if 
matter  exists,  it  is  impossible  for  us  to  know 
the  fact,  or  to  know  anything  about  it.  But 
this  conclusion  he  habitually  uses  as  equivalent 
to  the  proposition  that  "  matter,  in  fact,  does 
not  exist,"  i.  e.,  he  substitutes  the  "  non- 
existence  of  matter"  for  "  ignorance  of  its 
existence." 


CHAPTER  XIII 

ILLICIT  CONVERSIONS 

§  183.  SIMPLE  CONVERSION  OF  UNIVERSAL 
AFFIRMATIVE  PROPOSITION. — The  most  usual 
form  of  this  fallacy  occurs  in  the  simple  con- 
version of  a  universal  affirmative  proposition, 
as,  e.  g.,  where  from  the  proposition  Y  is 
X  "  we  illicitly  infer  that  "  X  is  Y  " ;  and  to 
this  form  all  other  cases  may  be  reduced.  The 
fallacy  is  so  obvious  that  it  might  be  supposed 
it  could  not  often  occur,  but  it  is  in  fact  very 
common. 

Examples 

§  184.  CONFUSION  OF  PROPOSITION  WITH 
JUDGMENT. — An  example  of  it  seems  to  be 
presented  by  the  commonly  received  doctrine 
that  "  a  proposition  is  a  judgment  expressed  in 
words  ";  which  seems  to  result  from  an  illicit 
conversion  of  the  proposition  that  a  "  judg- 
ment expressed  in  words  is  a  proposition." 

§  185.  ILLICIT  CONVERSION  BY  NEGATION. 
198 


ILLICIT  CONVERSIONS  199 

—The  fallacy  frequently  occurs  in  the  conver- 
sion of  a  proposition  by  negation  or  contra- 
position. Thus,  c.  g.,  the  proposition  "  Y  is 
not  X  "  becomes  by  negation  "  Y  is  not-X  "  ; 
from  which — converting  per  accidens — we  may 
infer  that  "  Some  not-X  is  Y  " ;  but  not — as  is 
often  inferred— that  "  All  not-X  is  Y." 

By  this  method  any  universal  affirmative 
proposition  ("  Y  is  X  ")  may  be  converted  into 
a  proposition  between  the  negatives  of  its  terms 
(i.  e.,  Not  X  is  not  Y) ;  but  not,  as  is  often 
done,  without  converting  the  terms, —  i.  e., 
from  the  proposition  "  Y  is  X  "  we  may  infer 
that  "  Not  X  is  not  Y,"  but  not  that  "  Not 
Y  is  not  X  "  (§  91). 

§  1 86.  AN  ARGUMENT  OF  HOBBES. —  A 
striking  example  of  this  fallacy  is  presented  by 
Hobbes,  that  prince  of  logicians.  Justice  he 
defines  as  the  keeping  of  covenants,  and  injus- 
tice as  the  failure  to  keep  them.  But,  accord- 
ing to  his  theory,  covenants  become  valid  only 
upon  the  institution  of  government,  from  which 
they  derive  their  validity.  Hence  in  a  state  of 
nature  there  is  neither  justice  nor  injustice. 
But  he  says  also:  "  Whatever  is  not  unjust  is 
just,"  and  this  conclusion  —  which  is  contra- 
dictory to  his  main  position  —  is  obviously 
arrived  at  by  an  illicit  conversion  of  the  univer- 
sal affirmative  proposition,  "  Whatever  is  just 
is  not-unjust." 


CHAPTER  XIV 

ILLICIT   SUBSTITUTIONS   OF   TERMS 

§  187.  Substitutions  of  terms  may  consist 
either  in  the  substitution  of  a  new  vocable  or 
vocal  sign,  or  in  the  substitution  of  a  new 
sense  to  the  same  vocable.  The  latter  is  always 
illicit,  and  constitutes  the  Fallacy  of  Equivoca- 
tion. The  former  will  be  considered  in  this, 
the  latter  in  our  next  chapter. 

The  substitution  of  new  terms  of  equivalent 
signification  for  terms  originally  occurring  is 
the  most  common  and  extensive  in  application 
of  all  the  processes  involved  in  ratiocination; 
and  the  corresponding  illicit  processes  —  if  we 
include  equivocation  —  may  be  regarded  as  in- 
cluding all  fallacies  whatever.  Hence  the 
examples  already  given,  and  especially  those 
given  under  the  head  of  Irrelevant  Conclusion, 
will  serve  equally  well  to  illustrate  the  fallacy 
now  under  consideration. 

Examples 

§  188.  AUSTIN'S  ARGUMENT. —  Many  ex- 
amples of  this  fallacy  are  furnished  by  Austin, 


ILLICIT  SUBSTITUTION  2OI 

as,  e.  g.,  in  substituting  for  the  predicate  of  the 
proposition  that  "  The  sovereign  power  is  in- 
capable of  legal  limitation ,"  the  term  "  legally 
despotic,"  and  thus  inferring  from  the  former 
proposition  that  government  is  vested  by  law 
with  despotic  power;  which  is  not  only  untrue, 
but  upon  his  own  theory  impossible.  For,  if 
law  is  but  an  expression  of  the  will  of  the 
sovereign,  it  is  equally  absurd  to  say  either 
that  the  sovereign  power  "  is  limited"  or  that 
"  it  is  conferred"  by  law. 

§  189.  SPENCER'S  ARGUMENT. —  Another 
example  is  furnished  by  Spencer  in  inferring 
from  the  "  right  of  free  exchange  "  the  "  right 
of  free  contract,"  which  is  in  effect  to  substitute 
genus  for  species  in  the  subject  of  a  universal 
affirmative  proposition.  For  exchange  is  only 
a  species  of  contract  (v.  supra,  §  181).  It  is  true 
that  the  right  of  free  contract  cannot  be 
doubted,  but  the  substitution  is  none  the  less 
a  logical  fallacy. 

§  190.  FLETCHER  vs.  PECK. — Still  another 
example  of  this  fallacy  is  furnished  by  Chief- 
Justice  Marshall  (the  greatest  and  most  logical 
of  American  jurists)  in  Fletcher  vs.  Peck,  6 
Cranch,  135  ;  where  it  was  decided  that  an  act 
of  the  Legislature  of  Georgia  revoking  a  grant 
of  land  was  in  contravention  of  the  provision  of 
the  Constitution  of  the  United  States  forbid- 
ding the  States  to  pass  any  act  "  impairing 


202 


LOGIC 


the  obligation  of  contracts.'"  The  argument  in 
effect  was  that  a  grant  is  a  contract,  and  that 
this  was  impaired  by  the  act ;  which  was  in 
effect  to  substitute  "  Contract"  for  "  Obliga- 
tion of  Contract."'  The  fallacy  is  the  more 
glaring  from  the  fact  that  a  grant  is  an  exe- 
cuted contract,  which  carries  with  it  no  obliga- 
tion. Hence  the  constitutional  provision  must 
be  held  to  refer  only  to  executory  or  obligatory 
contracts. 


CHAPTER  XV 

EQUIVOCATION 

§  191.  The  ambiguity  of  terms  and  sentences 
(Homonymia  et  AmpJiibolid)  is  undoubtedly  the 
most  prolific  of  all  sources  of  fallacy.  This  is 
recognized  by  all  logicians,  and,  indeed,  by 
philosophers  generally ;  but  we  doubt  that 
many  appreciate  the  extent  of  the  evil  or  the 
universality  of  the  danger  to  which  men  are 
exposed  by  reason  of  it,  or  (especially)  their 
own  infirmity  in  this  respect. 

'  Instances  of  this  fallacy,"  says  Mr.  Mill, 
"  are  to  be  found  in  most  all  the  argumentary 
discourses  of  imprecise  thinkers";  a  proposi- 
tion true  in  its  literal  statement  but  false  in  its 
obvious  implications;  for  it  implies  that  the 
proposition  is  not  true  of  precise  thinkers,  and 
also  (though  with  becoming  modesty)  that  it  is 
not  true  of  the  author.  But  in  fact  the  most 
precise,  or,  as  we  would  prefer  to  say,  the 
most  logical  thinkers  are  liable  to  fallacy,  and 
especially  to  this  kind  of  fallacy ;  and  none 
203 


204  LOGIC 

more  so  than  Mr.  Milh1  In  this  respect,  if 
fallacies  be  regarded  as  intellectual  sins,  we 
may  say:  "  There  are  none  righteous.  No, 
not  one."  For  it  is  with  logicians  as  with 
generals:  the  best  that  can  be  said  of  them  is, 
that  the  greatest  are  those  who  commit  the 
fewest  blunders.  Hence  the  only  difference, 
other  than  degree,  between  the  more  precise  or 
logical  thinker  and  the  unprecise  is,  that  the 
fallacies  of  the  latter  are  difficult,  those  of  the 
former  easy  to  expose.  Hence  it  may  be  said 
that,  while  it  is  the  greatest  achievement  to  be 
right,  it  is  no  mean  achievement  to  be  clearly 
and  unequivocally  wrong,  i.  e.,  perspicuous  in 
our  errors.  Hence  the  value  of  the  political 
theories  of  Hobbes  and  Austin,  the  most  logi- 
cal of  modern  writers;  which,  though  false, 
and  even  pernicious,  are  yet  full  of  instruction. 
Nor  is  the  proportion  of  men  of  great  logical 
genius  so  large  as  is  generally  supposed.  They 
are  in  fact  as  scarce  as  great  generals,  or  great 
statesmen,  or  great  poets.  Nor  is  it  to  be  as- 
sumed that  philosophical  writers  are  less  liable 
to  this  and  other  fallacies  than  the  less  preten- 
tious classes.  '  For  it  is  most  true,  as  Cicero 
saith  of  them  somewhere,  that  there  can  be 
nothing  so  absurd  but  may  be  found  in  the 
books  of  the  Philosophers"  (Hobbes, 


1  This  is  very  fully  shown  by  Mr.  Jevons  (Pure  Logic  and 
Minor  Works,  p.  201). 


EQUIVOCATION 

v.).  So,  as  observed  by  the  author  cited,  the 
educated  classes  generally  are  inferior  to  the 
vulgar  in  this  respect.  For  "  those  men  that 
take  their  instruction  from  the  authority  of 
books,  and  not  from  their  own  meditations, 
[are]  as  much  below  the  condition  of  ignorant 
men  as  men  endued  with  true  science  are  above 
it.  For  between  true  science  and  erroneous 
doctrines,  ignorance  is  in  the  middle  "  (/</., 
chap.  iv.).  Hence  no  one  should  imagine  him- 
self free  from  this  general  infirmity  of  mankind  ; 
and  he  who  most  thoroughly  realizes  his  weak- 
ness in  this  respect  may,  like  Socrates,  be  justly 
pronounced  the  wisest  of  mankind.  All  are 
liable  to  it;  and  he  who  supposes  he  is  not  is 
simply  unaware  of  his  infirmity. 

The  nature  of  the  Fallacy  of  Equivocation  is 
obvious,  and  has  been  sufficiently  explained. 
It  remains,  therefore,  only  to  illustrate  it  by 
appropriate  examples,  and  for  this  purpose  the 
examples  already  given  under  other  heads  will 
— with  one  or  two  others — be  sufficient  to  serve 
our  purposes. 

Examples 

§  192.  EQUIVOCAL  USE  OF  NONSENSICAL 
TERMS. — Some  of  the  most  important  cases  of 
this  fallacy  occur  from  the  use  of  nonsensical 
terms.  The  very  nature  of  these  is  that  they 


2O6  LOGIC 

cannot  be  used  for  any  practical  purpose,  ex- 
cept by  changing  their  meaning  and  thus 
giving  them  a  definite  sense;  and  hence,  for 
the  propositions  in  which  they  occur,  significant 
propositions  are  always  substituted.  Thus,  as 
we  have  seen,  the  term  Sovereignty  varies  es- 
sentially in  meaning,  as  used  in  the  several 
doctrines  of  Personal  Sovereignty,  Corporate 
Sovereignty,  the  Sovereignty  of  the  People  or 
State,  and  the  Sovereignty  of  Right  or  the  Law  ; 
all  of  which  different  senses  of  the  term  are  in- 
consistent with  each  other,  and  all,  except  the 
first,  in  their  direct  sense,  without  definite 
signification,  or,  in  other  words,  nonsensical. 
Yet  the  term  is  habitually  used  by  political 
writers  without  distinguishing  the  sense  in 
which  it  is  used,  or  without  attempting  to  give 
it  any  definite  signification.  But  in  the  prac- 
tical application  of  the  doctrine  of  Sovereignty 
the  term  is  invariably  used  as  equivalent  to 
such  definite  conclusions  as  the  occasions  of 
the  writer  may  require,  or  as  a  premise  from 
which  such  conclusions  may  be  deduced;  and 
thus  the  most  extravagant  doctrines  are  ap- 
parently established.  Of  which,  as  we  have 
seen,  a  striking  example  is  furnished  by  Prof. 
Von  Hoist  (§  175);  and  others  equally  ap- 
propriate may  be  easily  collected  from  almost 
any  work  touching  the  subject. 

The    same    observation    will   apply   to   the 


EQUIVO CA  TION  2O/ 

theory  of  general  utility,  or  Utilitarianism, 
and  also  to  the  notions  that  the  will  of  the 
government  is  the  united  will  of  the  people  ; 
that  the  State  is  an  Organism ;  that  it  is 
founded  on  compact,  etc.  ;  all  of  which  are,  in 
their  direct  sense,  in  themselves  nonsensical, 
and  therefore  innocuous,  but  are  habitually 
used  as  premises  to  establish  all  sorts  of  ex- 
travagant conclusions. 

§  193.  OF  EQUIVOCATION  GENERALLY.— 
The  above  will  suffice  for  examples  of  equiv- 
ocations consisting  in  giving  significance  to 
nonsensical  terms.  In  illustrating  other  equiv- 
ocations, the  only  embarrassment  consists  in 
the  number  of  examples  that  crowd  upon 
our  attention ;  but  the  following  may  be 
sufficient. 

§  194.  ARGUMENT  OF  AUSTIN. — One  of  the 
most  striking  of  these  is  furnished  us  by  the 
argument  of  Austin  in  support  of  his  famous 
position  that  judicial  decisions  are  in  their 
essential  nature  laws  or  statutes,  and  the  judges, 
in  fact,  legislators;  and  another  by  his  equally 
remarkable  position  that  "  Custom  does  not  con- 
stitute part  of  the  law"  ;  both  of  which  rest 
upon  the  equivocal  use  of  the  ambiguous  term 
"  Law  "  ;  which  may  denote  either  a  law  or 
statute  (lex],  or  the  Law  (Jus). 

§  195.  AN  ARGUMENT  OF  BAIN. — An  ex- 
tremely effective  example  of  this  fallacy  is  also 


208  LOGIC 

furnished  by  Mr.  Bain  in  his  statement  of  the 
doctrine  of  Utility.  It  consists  in  using  the 
term  "party  "  in  the  double  sense  of  a  natural 
and  of  a  corporate  person.  Utility,  he  says,  is 
"  the  tendency  of  actions  to  promote  the  happi- 
ness and  prevent  the  misery  of  the  party  under 
consideration;  which  party  is  usually  the  com- 
munity in  which  one's  lot  is  cast."  ' 

§  196.  AN  ARGUMENT  ATTRIBUTED  TO 
PROFESSOR  HUXLEY. — Still  another  example 
is  presented  by  an  argument  attributed  to  Pro- 
fessor Huxley.  It  consists  in  the  equivocal  use 
of  the  term  "power,'"  which  is  commonly  used 
in  two  senses,  namely,  as  denoting  actual  power, 
or  might,  and  as  denoting  rightful,  or  jural, 
power,  or  right.  The  argument  is  as  follows: 
'  The  power  of  the  State  may  be  defined  as 
the  resultant  of  all  the  social  forces  within  a 
definite  area.  It  follows,  says  Professor  Hux- 
ley, with  characteristic  logical  thoroughness,  that 
no  limit  is  or  can  be  set  to  State  interference  " 
(A  Plea  for  Liberty,  Donisthorpe). 

This  fallacy  is  common  to  all  the  Austinian 
school  of  jurists,  and,  indeed,  constitutes  the 
common  fundamental  infirmity  of  all  their  dis- 
quisitions. These  jurists,  according  to  their 
theory,  have,  indeed,  no  right  to  use  the  term 
in  any  but  the  former  sense;  but,  as  we  have 

1  Bentham  is  guilty  of  the  same  fallacy  (Principles  of  Legis- 
lation). 


EQUIVOCATION 


209 


seen,  after  establishing  their  conclusions  they 
habitually  use  it  as  though  equivalent  to  right, 
in  the  proper  sense — a  notion  that  can  properly 
have  no  place  in  their  system. 


CHAPTER  XVI 

THE   TRADITIONAL    DOCTRINE    OF   FALLACIES 

I 
ARISTOTLE'S  CLASSIFICATION  OF  FALLACIES 

§  197.  The  received  classification  of  fallacies, 
— adopted  by  the  schoolmen  from  Aristotle,— 
though  remarkable  for  its  profound  insight,  has 
but  few  pretensions  to  scientific  accuracy;  and 
it  is  to  be  suspected  that  much  of  the  obscurity 
and  confusion  that  surround  the  subject  results 
from  the  undue  authority  given  to  it  by  logi- 
cians. It  has,  however,  so  profoundly  affected 
logical  doctrine  and  nomenclature  that,  apart 
from  its  intrinsic  value,  it  must  always  remain 
one  of  the  principal  subjects  for  the  student's 
attention. 

§  198.  TABLE  OF  FALLACIES. — According 
to  this  scheme,  fallacies  are  divided  into  two 
classes,  called  by  the  schoolmen  and  by  later 
logicians,  Fallacies  in  Dictione,  or  in  Voce  (i.  e., 
in  diction  or  speech),  and  Fallacies  extra  Dic- 
tionem,  or  in  Re  (i.  e.,  not  in  diction,  but  in 

210 


DOCTRINE   OF  FALLACIES  211 

matter).  Of  the  former  class  six  forms  or 
examples  are  given,  and  of  the  latter,  seven, 
which  are  as  follows: 

Aristotle ' s  Division  of  Fallacies 

I.  FALLACIES  IN  DICTIONE  : 

(i)  Homonymia  (Ambiguity  of  Terms). 
(*)  Amphibolia  (Ambiguity  of  Sentence). 

(3)  F.  Compositions  (F.  of  Composition). 

(4)  F.  Divisionis  (F.  of  Division). 

(5)  F.  Accentus  (F.  of  Accent). 

(6)  F.   Figures   Dictionis    (F.    of    Figure    of 

Speech). 

II.  FALLACIES  EXTRA  DICTIONEM  : 

(1)  F.  Accidentis  (F.  of  Accident). 

(2)  F.  a  Dicto  Secundum  Quid  ad  Dictum  Sim- 

pliciter  (Illicit  Substitution  of  Unquali- 
fied for  Qualified  Terms). 

(3)  Ignoratio  Elenchi  (Irrelevant  Conclusion). 

(4)  F.  Consequents  (Non-Sequitur). 

(5)  Petitio  Principii  (F.  of  Illicit  Premise). 

(6)  Non-Causa pro  Causa  (Mistaking  Cause). 

(7)  F.  Plurium  Interrogationum  (F.  of  Several 

Issues  in  One). 

§  199.  OBSERVATIONS  UPON  THIS  CLASSI- 
FICATION.— As  will  be  seen  presently,  all  the 
fallacies  In  Dictione  are  simply  cases  of  Equivo- 
cation, and  of  the  fallacies  Extra  Dictionem  all 
except  the  4th  (F.  Consequentis)  are  Fallacies 
of  Judgment ;  under  which  head  most  of  them 
have  already  been  considered  at  large.  The 


212  LOGIC 

excepted  fallacy  (the  F.  Consequentis)  includes 
all  the  Fallacies  of  Inference,  except  Equivoca- 
tion. It  is  obvious,  therefore,  that  the  current 
expressions  (In  Dictione  and  Extra  Dictionetn) 
—whether  from  being  a  mistranslation  of  Aris- 
totle's language  or  otherwise  —  do  not  truly  ex- 
press the  nature  of  the  distinction  between  the 
two  kinds  of  fallacies,  and  are,  therefore,  cal- 
culated to  mislead  us  —  as  they  have  Whately 
and  others  —  with  regard  to  it. 

§  200.  The  true  scheme  of  division  is  as  fol- 
lows: 

Table  of  Fallacies 

I.  FALLACIES  IN  DICTIONE  (EQUIVOCA- 
TION). 

(Including  the  six  forms  specified  in  the 
first  table.) 

II.  FALLACIES  EXTRA  DICTIONEM. 
(i)  Fallacies  of  Judgment. 

(Including  all  fallacies  Extra  Dictionem 
given  in  the  table,  except  F.  Conse- 


(2) F.  Consequentis  (JVon-Sequitur). 

(Including  all  Fallacies  of  Inference  ex- 
cept Equivocation.) 

(a)  Formal  Fallacies  (/.  e.,  of  Inference). 
(Including    Undistributed    Middle,    Il- 

licit Process.) 

(b)  Material  Fallacies. 

(Including  Illicit  Substitutions  of  New 
Terms.) 


DOCTRINE   OF  FALLACIES  213 

The  terms  "Formal"  and  " Material  Fal- 
lacies" correspond  to  the  "Logical"  and 
"  Material  Fallacies  "  of  Whately,  whose 
"  Semi-logical  Fallacies  "  correspond  precisely 
to  the  fallacies  In  Dictione  of  Aristotle,  or,  in 
other  words,  to  the  Fallacy  of  Equivocation. 
This  division  of  Whately's  has,  since  his  time, 
been  very  generally  adopted ;  but,  as  is  re- 
marked by  Mansel,  it  "  is  not  the  ancient  prin- 
ciple of  distinction  which  is  stated  with  more 
or  less  clearness  by  several  logicians,"  as,  e.  g., 
in  the  following  definitions  of  Sanderson: 

Every  fallacy  In  Dictione  arises  from  some 
ambiguity  (mnltiplicitate}  of  expression." 
'  Fallacies  Extra  Dictionem  are  those  in  which 
the  deception  happens,  not  so  much  from  some 
ambiguity  latent  in  the  words  themselves,  as 
from  ignoring  things  "  (i.  e.,  the  notions  ex- 
pressed). '  The  former  arise,"  says  Mansel, 
"from  defects  in  the  arbitrary  signs  of  thought, 
and  hence  are  generally  confined  to  a  single  lan- 
guage, and  disappear  on  being  translated  into 
another.  The  latter  are  in  the  thought  itself, 
whether  materially,  in  the  false  application  of 
notions  to  things,  or  formally,  in  the  violation 
of  the  laws  by  which  the  operations  of  the 
reason  should  be  governed ;  and  thus  adhere 
to  the  thought  in  whatever  language  it  may  be 
expressed.  Under  this  head  are  thus  included 
both  false  judgments  and  illogical  reasonings" 


214  LOGIC 

(i.  e.,  both   Fallacies  of  Judgment   and    Fal- 
lacies of  Inference)  (Mansel's  Aldrich,  p.  132). 

II 

FALLACIES  IN  DICTIONS   (EQUIVOCATION) 

§  2OI  (l)  (2).  HOMONYMY  AND  AMPHI- 
BOLY.— These  are  both  cases  of  the  Fallacy  of 
Equivocation,  the  former  consisting  in  the 
illicit  use  of  ambiguous  terms,  the  latter  in  the 
illicit  use  of  ambiguous  sentences.  They  are 
essentially  of  the  same  nature;  and  we,  there- 
fore, as  is  most  in  accord  with  the  usage  of  our 
language,  class  them  together  under  the  com- 
mon name  of  Equivocations.  This  fallacy 
has  already  been  fully  considered. 

§  202  (3)  (4).  COMPOSITION  AND  DIVISION.— 
These  fallacies  are  essentially  of  the  same 
nature.  They  consist  in  using  a  term  succes- 
sively in  a  distributive  and  in  a  collective  sense, 
or,  in  other  words,  in  substituting  for  a  term 
used  distributively  the  same  term  used  collect- 
ively, or  vice  versa.  The  former  constitutes  the 
Fallacy  of  Composition,  the  latter  the  Fallacy 
of  Division. 

The  following  are  examples  of  the  Fallacy 
of  Composition : 

3  and  2  (distributively]  are  two  numbers ; 

5  is  3  and  2  (collectively)-, 

.'.  5  is  two  numbers. 

He  who  necessarily  ^tv-y  or  stays  (i.  e.,  either 


DOCTRINE   OF  FALLACIES  21$ 

necessarily  goes,  or  necessarily  stays)  is  not  a 
free  agent ; 

But  every  one  either  necessarily  ^w.?  or  stays 
(i.  e.,  necessarily  does  one  or  the  other); 

.  •.  No  one  is  a  free  agent. 

The  following  are  examples  of  the  Fallacy  of 
Division : 

5  is  one  number; 

3  and  2  (collectively)  are  5  ; 

.  *.  3  and  2  (distributively)  are  one  number. 

The  angles  of  a  triangle  are  equal  to  two 
right  angles ; 

A  B  C  is  an  angle  of  a  triangle ; 

.  •.  A  B  C  is  equal  to  two  right  angles. 

All  the  black  and  white  horses  of  the  de- 
ceased (/.  e. ,  all  the  black,  and  all  the  white 
horses)  are  the  property  of  the  legatee ; 

The  piebald  horses  are  black  and  white 
(/.  e. ,  each  is  black  and  white); 

.  •.  The  piebald  horses  are  the  property  of 
the  legatee.1 

Obviously  these  fallacies  (Composition  and 
Division)  constitute  merely  a  species  of  equivo- 
cation, i.  e.,  of  either  Homonymy  or  Amphiboly. 

1  The  last  example  is  suggested  by  the  celebrated  Moot  case 
of  the  legacy  of  "all  the  testator's  black  and  white  horses." 
The  question  was,  whether  the  legatee  was  to  have  the  black 
and  the  white  horses,  or  the  piebald  horses,  i.  e.,  the  horses 
that  were  each  black  and  white.  The  legatee  claimed  that  he 
was  entitled  to  both  classes  ;  and,  hence,  in  the  one  or  the 
other  of  his  claims,  was  guilty  of  this  fallacy. 


2l6  LOGIC 

§  203  (5).  THE  FALLACY  OF  ACCENT  OR 
PROSODY  (F.  ACCENTUS  F.  PKOSODI^E}. — 
This  fallacy  is  also  a  species  of  equivocation, 
i.  e.,  either  Homonymy  or  Amphiboly.  It  con- 
sists in  varying  the  meaning  of  a  term  or 
proposition  by  change  of  accent,  tone,  or 
punctuation. 

The  most  extreme  case  of  this  is  that  of 
irony,  by  which  the  sense  is  precisely  reversed, 
as,  e.  g.,  in  the  speech  of  Job  to  his  friends: 
"  No  doubt  but  you  are  the  people,  and  wis- 
dom shall  die  with  you."  In  this  way,  i.  e., 
by  ironical  use  afterwards  forgotten,  the  name 
of  the  subtle  doctor,  Duns  Scotus,  has  come 
to  be  the  peculiar  name  of  a  fool  (i.  e.,  dunce). 
The  fallacy  resulting  from  changing  the  sense 
of  an  ironical  expression  is  too  obvious  to  be 
dangerous,  but  if  it  should  occur  would  be  a 
case  of  F.  Figures  Dictionis. 

§  204  (6).  FIGURE  OF  SPEECH  (F.  FIGURE 
DICTIONIS}.  —  This  fallacy  (which  is  also 
merely  a  species  of  equivocation)  consists  in 
the  illicit  use  of  figures  of  speech,  or,  in  other 
words,  in  substituting  for  the  indirect  or  fig- 
urative, the  direct  or  literal  sense,  as  in  the 
following  example: 

"  Herod  is  a  fox  ; 
A  fox  is  a  quadruped  ; 
.'.  Herod  is  a  quadruped." 


DOCTRINE   OF  FALLACIES  21J 

Or  as  in  the  following  example,  which  was 
given  by  a  student  called  on  for  a  syllogism. 
The  logical  Professor,  it  may  be  explained, 
was  of  corpulent  habit,  and  known  as  "  Old 
Boll." 

"  All  flesh  is  grass,  the  Scriptures  say, 
And  grass  when  cut  is  turned  to  hay  ; 
Now  if  Death's  Scythe  Old  Boll  should  take, 
Golly  !    What  a  haystack  he  would  make  !  " 

But  more  serious  examples  may  be  found 
among  those  already  given,  as,  e.  g.,  the 
equivocal  use  of  the  term  poivcr  in  the  argu- 
ment attributed  to  Professor  Huxley,  and  also 
in  the  misuse  of  the  propositions  that  "  the 
State  is  a  person,"  that  "it  is  an  organism," 
that  "  its  ivill  is  the  united  will  of  the  people," 
that  "  it  has  an  interest  or  ivelfare  distinct 
from  that  of  the  people,"  etc.,  as  heretofore  ex- 
plained. A  striking  example  of  this  fallacy  is 
also  presented  in  the  famous  case  of  Dart- 
mouth College  vs.  Woodward  (§  137).  The 
fallacy  consisted  in  regarding  the  college  as 
a  person ;  which  was  only  figuratively  true. 
For  a  corporation  is  a  qua ^z'-person  only,  i.  c., 
is  regarded  as  a  person  for  certain  purposes 
only. 

§  205.  Hamilton  strangely  speaks  of  this  as 
"  a  contemptible  fallacy,"  and — as  though  to 
furnish  an  example  at  once  of  confusion  of 


2l8  LOGIC 

things  essentially  different  and  of  misappre- 
hension of  the  nature  and  scope  of  Logic — he 
couples  with  the  Fallacy  of  Figure  of  Speech 
that  of  Equivocation,  as  being,  the  latter,  a 
species  of  the  former,  instead  of  vice  versa,  as 
is  in  fact  the  case.  '  These  fallacies,"  he  says, 
(" '  sophismata  equivocationis,  anipliibolia,  et  ac- 
centus)  may  easily  be  reduced  to  sophismata 
figures  dictionis ;  they  are  only  contemptible 
modifications  of  this  contemptible  fallacy." 

But,  as  is  in  effect  observed  by  the  author  to 
whom  we  are  indebted  for  the  above  quota- 
tion, when  we  reflect  that  nearly  all  words 
denoting  mental  or  moral  qualities  or  acts— 
which  is  but  to  say  nearly  all  terms  used  in  the 
different  branches  of  the  science  of  human 
nature — are  in  their  origin  metaphors,  derived 
from  sensible  objects  or  events  as,  e.  g,,  intui- 
tion, perception,  appreJiension,  inference,  induc- 
tion, deduction,  reflection,  education,  justice, 
right,  wrong,  straight,  power,  organic,  etc., 
and  that  these  terms  still  carry  with  them,  to 
a  large  extent,  their  material  associations,  by 
which,  as  the  history  of  philosophy  shows,  we 
are  continually  being  misled,  we  can  hardly 
fail  to  agree  "  that  the  sophism  Figure  Dic- 
tionis, so  far  from  being  contemptible,  is 
worthy  of  our  closest  and  most  watchful 
consideration"  (Theory  of  Thought,  Davis,  p. 
27). 


DOCTRINE   OF  FALLACIES  21$ 

III 

OF    THE    FALLACIES   EXTRA    DICTIONEM 

§  206.  OBSERVATIONS. — Of  these  fallacies, 
all  except  the  fourth  are  Fallacies  of  Judgment ; 
and  four  of  them,  namely,  Ignoratio  Elenchi, 
Petitio  Principii,  Non  Causa  pro  Causa,  and  F. 
Plurium  Interrogationum,  have  already  been 
considered  in  detail  under  that  head.  The 
others,  namely,  the  Fallacies  of  Accident,  of 
Secundum  Quid,  and  of  the  Consequent — of 
which  the  first  two  are  also  Fallacies  of  Judg- 
ment— remain  to  be  considered. 

Logicians  are  widely  at  variance  with  refer- 
ence to  the  nature  of  these  fallacies;  and,  if 
we  may  judge  from  the  translations  and  from 
the  confusion  reigning  over  the  subject,  Aris- 
totle's own  explanation  of  them  must  be  re- 
garded, in  some  particulars,  as  hopelessly 
obscure.  Hence,  though  I  have  attempted  to 
interpret  his  meaning  correctly,  I  am  by  no 
means  sure  that  I  have  succeeded  in  this  better 
than  others.  It  may,  however,  be  claimed  for 
the  exposition  of  the  subject  here  given  that  it 
is  at  least  intelligible  and  consistent,  and  that, 
in  connection  with  the  rest  of  Aristotle's 
scheme,  it  renders  his  classification  of  the  fal- 
lacies complete.  And,  it  may  be  added,  it  is 
in  accord  with  the  best  authorities. 


22O  LOGIC 

§  207.  THE  FALLACY  OF  ACCIDENT  CF.  Ac- 
CIDENTis}.—T:\\\s  fallacy  has  its  source  in  the 
assumption  that  an  accident  of  some  of  the 
significates  of  a  term,  or  of  all  its  significates 
for  a  certain  time,  is  an  accident  of  the  term, 
and  therefore  predicable  of  it  without  qualifi- 
cation (v.  supra,  §  49.)  This  assumption  in 
the  case  of  an  inseparable  accident  of  all  the 
significates  of  the  term  is,  indeed,  legitimate; 
for  obviously  such  an  accident  may  always  be 
predicated  of  all  the  significates  of  the  term, 
and  hence  of  the  term.  But  with  separable  ac- 
cidents of  the  significates  of  a  term,  it  is  other- 
wise; for,  though  these  are  commonly  spoken 
of  as  accidents  of  the  term,  they  are  not  such 
in  fact,  for  their  relation  to  the  term  is  tem- 
porary or  transient.1  Hence  such  an  accident 
can  be  predicated  of  the  term  only  for  so  long 
as  it  continues  to  be  an  accident  of  it,  or,  in 
other  words,  only  with  relation  to  some  par- 
ticular time  expressed  or  understood.  For  in 
the  logical  proposition  the  copula  has  no  rela- 
tion to  time,  but  expresses  simply  a  permanent 
significative  relation  between  the  terms,  and 

1  The  terms  separable  and  inseparable  accidents  can  apply 
only  to  real  individuals,  and  hence  only  to  concrete  terms  or 
terms  of  first  intention.  With  relation  to  these  the  distinc- 
tion is  sufficiently  obvious.  Thus,  e.  g.,  with  reference  to 
Socrates,  "  Stagyrite"  is  an  inseparable  accident ;  "standing," 
"sleeping,"  etc.,  separable — the  last  being  predicable  of  him 
only  at  times. 


DOCTRINE   OF  FALLACIES  221 

hence  a  separable  accident  cannot  be  predi- 
cated generally  of  a  term.  For,  as  is  said  by 
Aristotle,  "  it  is  uncertain  when  [i.  e.,  at  what 
times]  an  assertion  can  be  made  of  a  thing 
present  from  accident";  or,  in  other  words, 
whether  at  any  given  time  the  accident  con- 
tinues to  exist  (Soph.  Elenc/i,  chap.  xxiv.). 
Thus,  e.  g,,  an  attacking  party  might  be  rightly 
informed  at  a  given  time  that  the  enemy  was 
sleeping,  and  hence  conclude  that  it  would  be 
safe  to  attack  him;  but  it  might  be  a  fatal 
error  to  assume  the  truth  of  the  premise  as 
continuing  to  exist  an  hour  later. 

§  208.  DEFINITION  OF  THE  FALLACY. — The 
fallacy  may  therefore  be  defined  as  consisting 
in  predicating  of  a  term  a  separable  accident  of 
its  significates  without  qualifying  it  by  refer- 
ring to  the  time  at  or  during  which  it  is  inher- 
ent ;  or,  in  other  words,  in  assuming,  in  place  of 
a  proposition  of  which  the  predicate  is  an  ac- 
cident thus  qualified,  another  proposition  of 
which  the  predicate  is  the  accident  unqualified  ; 
as  if,  e.  g.,  from  knowing  a  man  is  lame  we 
should  assume  that  he  is  permanently  lame. 
Or  the  subject  may  be  more  generally  illus- 
trated as  follows:  Let  Y  denote  the  subject 
("  John  "),  A  the  accidental  predicate  ("  tem- 
porarily lame,"  i.  e.,  "lame  for  the  time  being"), 
and  X  the  general  predicate  (^'permanently 
lame  ");  then  we  may  be  entitled  to  say  "  Y 


222  LOGIC 

is  A  " ;  but  to  assume,  in  place  of  this,  that 
Y  is  X  would  be  to  substitute  for  A  the  term 
X,  i.  e.,  species  tor  gemis  in  the  predicate  of  a 
universal  affirmative  proposition.  For  the 
class  of  "  temporarily  lame"  will  include  all 
the  "permanently  lame,"  and  many  others. 

It  will  be  noted  here  that  there  is  necessarily 
a  significative  relation  between  the  accidental 
and  the  general  predicate,  namely,  that  of 
partial  coincidence.  Hence,  to  substitute  X 
for  A  is,  in  effect,  to  substitute  AX  (i.  e., 
"  Some  A  ")  for  A,  which  presents  a  case  of 
illicit  substitution  of  species  for  genus  in  the 
predicate  of  an  affirmative  proposition. 

It  will  also  be  observed  that  the  Fallacy  of 
Accident  is  defined  as  consisting  in  the  illicit 
assumption  of  a  premise.  But,  where  the  same 
fallacy  occurs  in  a  formal  inference,  it  con- 
stitutes the  Fallacy  of  Undistributed  Middle, 
which  is  a  case  of  Non-sequitur  or  F.  Consequen- 
tis,  as  may  be  thus  illustrated : 


Some  A  is  X 

Y  is  A 

.'.  Y  is  X 


The  stock  example  of  this  fallacy,  which  I 
have  taken  from  Aldrich,  is  as  follows: 

'  What  you  have  bought  you  have  eaten ; 
you   have    bought    raw    meat;    therefore   you 


DOCTRINE    OF  FALLACIES  22  3 

have  eaten  raw  meat  "  (Quod  emisti  comedisti  ; 
crudum  emisti  ;  ergo  crudum  comedisti);  which 
may  be  expressed  in  the  following  syllogism, 
which,  in  form,  is  unobjectionable: 

The  meat  you  buy  is  raw  ; 
The  meat  you  eat  is  the  meat  you  buy  ; 
.'.  The  meat  you  eat  is  raw. 

The  fallacy  here  may  be  regarded  as  a  case 
of  equivocation,  consisting  in  the  use  of  the 
term  "  raw  "  in  the  major  premise  in  the  sense 
of  "  raw  when  bought,"  and  in  the  conclusion 
in  the  sense  of  "  raw  when  eaten."  But  if  the 
term  "  raiv  "  be  construed  simply  in  both 
cases  (/.  e.,  as  used  without  qualification),  the 
fallacy  must  be  regarded  as  a  case  of  F.  Acci- 
dentis,  consisting  in  the  illicit  assumption  of 
the  major  premise.  For  all  that  can  be  right- 
fully affirmed  is  that  the  meat  bought  is  raw  at 
the  time  of  purchase;  instead  of  which  it  is 
assumed  that  it  is  permanently  raw.  For, 
as  we  have  observed,  in  the  logical  prop- 
osition the  copula  includes  both  the  future 
and  the  past,  and  the  significative  relation  be- 
tween the  terms  is  asserted,  not  as  true  only 
at  the  moment  of  assertion,  but  before  and 
afterwards;  and  hence  a  universal  proposition 
may  always  be  negatived  by  showing  an  in- 
stance to  the  contrary,  either  in  the  past  or  in 
the  future. 


224  LOGIC 

The  following  examples  are  furnished  us  by 
Aristotle,  and  are  given  as  paraphrased  in  the 
notes  of  Mr.  Owen's  translation  : 

"  Do  you  know  what  I  am  about  to  ask  ? 
No.  But  I  am  about  to  ask  whether  virtue  is 
good.  Therefore,  you  know  not  whether  virtue 
is  good." 

"  Do  you  know  who  approaches  ?  No. 
But  Socrates  approaches.  Therefore,  you  do 
not  know  Socrates." 

Here  in  each  case  the  most  obvious  source 
of  the  fallacy  is  in  the  use  of  the  equivocal 
terms,  "  What  I  am  about  to  ask  "  (in  the 
first  case),  and  "  Who  approaches "  (in  the 
second).  But  this  ambiguity  may  be  removed 
and  the  arguments  expressed  syllogistically  in 
unobjectionable  form  as  follows: 

1 i )  The  question,  I  am  about  to  ask,  is  unknown  to 

you. 
The  question  whether  virtue  is  good  is  the  question 

I  am  about  to  ask. 

.'.  The  question  whether  virtue  is  good  is  unknown 
to  you. 

(2)  The  man  approaching  is  unknown  to  you. 
Coriscus  is  the  man  approaching. 

.'.  Coriscus  is  unknown  to  you. 

Indeed,  even  as  thus  expressed,  the  most 
obvious  solution  of  both  these  fallacies  is  still 
to  regard  them  as  cases  of  equivocation,  con- 


DOCTRINE   OF  FALLACIES  22$ 

sisting  in  using  the  term  "  unknown  to  you  "  in 
a  double  sense,  i.  e.,  in  the  major  premise  in 
the  sense  of  "  unknown  to  you  before  you  are 
told,"  and  in  the  conclusion  in  the  sense  of 
"  unknown  to  you  after  you  are  told,"  But  if 
the  term  be  regarded  as  used  in  the  same  sense 
in  both  places,  the  case  is  evidently  one  of  F. 
Accidenlis,  consisting  in  the  illicit  assumption 
of  the  major  premise,  or,  in  other  words,  in 
the  illicit  substitution  of  the  unqualified  term, 
"  unknown  to  you,"  for  the  qualified  term, 
"  unknown  to  you  before  you  are  told,"  which 
alone  was  admissible  as  a  predicate. 

§  209.  THE  FALLACY  OF  SECUNDUM  QUID 
(F.  A  DIC TO  SECUNDUM  QUID  AD  DICTUM 
SIMPLICITEK], — This  fallacy  consists  in  as- 
suming an  unqualified  in  place  of  a  qualified 
proposition.  But  as  the  copula  has  but  one 
meaning,  a  proposition  can  be  qualified  in  no 
other  way  than  by  qualifying  one  or  both  of 
its  terms.  Hence  the  fallacy  must  consist  in 
substituting  for  an  unqualified  a  qualified  term. 

But  a  term  can  be  qualified  (i.  e.,  its  signifi- 
cation or  extension  altered)  only  by  coupling 
with  it  another  term  that  partly,  but  not 
wholly,  includes  it,  thus  making  a  new  term  of 
less  extension,  as,  e.  g.,  men  by  white,  which 
gives  us  for  the  new  term,  white  men;  or, 
more  generally,  Z,  Y,  or  X,  by  A,  which 

gives  us,  for  new  terms,  AZ,  AY,  and  AX,  all 

15 


226  LOGIC 

included  in,  but  of  less  extension,  than  the 
originals;  or,  in  other  words,  the  class  denoted 
by  a  qualified  term  will  always  be  a  species 
of  the  class  denoted  by  the  unqualified  term. 
Hence  the  Fallacy  of  Secundum  Quid  is  simply 
a  particular  case  of  the  illicit  substitution  of 
genus  for  species  in  the  subject  of  an  affirmative, 
or  in  either  the  subject  m  predicate  of  a  negative 
proposition. 

Where  the  illicit  substitution  occurs  in  the 
inference,  the  fallacy  belongs  to  the  general 
class  of  fallacies  that  go  by  the  name  of  F. 
Consequentis  or  Non-scquitur ;  but  if  in  one 
of  the  premises,  it  constitutes  the  Fallacy  of 
Secundum  Qiiid,  now  under  consideration; 
which  must,  therefore,  like  the  F.  Accidentis, 
be  regarded  as  a  case  of  Illicit  Assumption  of 
Premise,  or  of  Petitio  Principii.  The  Fallacy 
of  Secundum  Quid  may  therefore  be  defined  as 
consisting  in  the  illicit  assumption  of  a  premise 
in  which  there  is  an  unqualified  term  in  place 
of  another  in  which  the  same  term  is  qualified ; 
or,  as  expressed  by  Aristotle,  is  assuming  that 
"  what  is  predicated  in  part  is  spoken  simply  " 
(Soph.  Blench.,  chap.  v. ,  2). 

§  210.  OF  THE  RELATION  BETWEEN  THE 
FALLACIES  OF  ACCIDENT  AND  SECUNDUM 
QUID. — The  Fallacy  of  Secundum  Quid  will 
therefore  include  the  Fallacy  of  Accident, which 
is  but  a  particular  case  of  it.  Or,  in  other 


DOCTRINE   OF  FALLACIES 


words,  the  latter  is  a  species  of  the  former,  its 
specific  difference  being  that  the  qualification 
omitted  relates  exclusively  to  time  ;  whereas, 
in  the  case  of  Secundum  Quid  generally,  the 
omitted  qualification  may  relate  either  to  time 
or  to  place,  quantity,  or  any  other  quality  or 
attribute. 

The  following  examples  of  the  F.  Secundum 
Quid  are  taken  from  various  sources  : 

(1)  Pernicious  things  are  things  to  be  forbidden; 
The  use  of  wine  is  pernicious  ; 

Therefore  the  use  of  wine  is  a  thing  to  be  for- 
bidden. 

(2)  Things  productive  of  bad  effects  are  unfit  for 

use  ; 

Antimony  is  a  thing  productive  of  bad  effects  ; 
.'.  Antimony  is  unfit  for  use. 

(3)  Things  productive  of  bad  effects  are  to  be  dis- 

couraged ; 

Eloquence  is  a  thing  that  produces  bad  effects  ; 
.'.  Eloquence  is  to  be  discouraged. 

(4)  Things   destructive   to  human    life  are   to    be 

avoided  ; 

Medicine  is  a  thing  destructive  to  human  life  ; 
.'.  Medicine  is  to  be  avoided. 

(5)  Y  is  X 
Z  is  Y 

/.  Z  is  X. 


228  LOGIC 

In  each  of  these  arguments — all  of  which  are 
regular  in  form  —  the  fallacy  consists  in  the 
illicit  assumption  of  the  minor  premise,  consist- 
ing in  substituting  in  the  subject  an  unqualified 
in  the  place  of  a  qualified  term,  viz.,  in  the 
first,  the  term  "  use  "  for  "  excessive  use";  in 
the  second,  "  antimony"  for  "  antimony  when 
misapplied" ;  in  the  third,  "eloquence"  for  "elo- 
quence when  abused" ;  in  the  fourth,  "  medi- 
cine" for  "  medicine  when  used  by  ignorant 
doctors" ;  and  in  the  fifth, — denoting  by  A  any 
term  qualifying  Z, — Z,  for  AZ.  The  fallacy, 
therefore,  in  each  case  consists  in  the  substitu- 
tion of  genus  for  species  in  the  subject  of  an 
affirmative  proposition,  and  hence  differs  from 
the  corresponding  fallacy  of  inference  simply 
in  being  an  illicit  assumption  instead  of  a 
formal  inference. 

§211.  ERRONEOUS  VIEWS  OF  LOGICIANS 
AS  TO  THESE  FALLACIES. — The  F.  Accidentis 
was  defined  by  Aldrich,  and  probably  by  the 
old  logicians  generally,  as  in  the  text.  But 
Whately,  who  is  followed  by  most  of  the  later 
logicians,  defines  it  as  the  converse  of  the 
Fallacy  of  Secundum  Quid ;  and  since  then  the 
subject  has  been  involved  in  the  greatest  con- 
fusion. The  prevailing  view  is  thus  expressed 
by  De  Morgan : 

"  (i)  The  Fallacia  Accidentis  and  (2)  that 
a  dicto  sccundum  quid  ad  dictum  simplicitcr. 


DOCTRINE   OF  FALLACIES  229 

The  first  of  these  ought  to  be  called  that  of 
a  dicto  simpliciter  ad  dictum  sccundum  quid,  for 
the  two  are  correlative  in  the  manner  described 
in  the  two  phrases.  The  first  consist  in  infer- 
ring of  the  subject  with  an  accident  that  which 
was  premised  of  the  subject  only,  the  second  in 
inferring  of  the  subject  only  that  which  was 
premised  of  the  subject  with  an  accident  "  (For- 
mal Logic,  p.  250). 

The  latter  process  is  undoubtedly  fallacious, 
but  the  former—/,  e.,  inferring  of  the  subject 
^vitJl  an  accident  that  which  was  premised  of 
the  subject  only  ;  or,  in  other  words,  of  infer- 
ring that  what  is  predicated  of  a  term  generally 
may  be  predicated  of  the  term  as  qualified  by 
an  accident  —  is  entirely  legitimate.  For  to 
qualify  a  term,  either  by  an  accident  or  other- 
wise, is  simply  to  diminish  its  extension,  and 
thus  to  create  a  subclass  or  species  of  the  class 
denoted  by  the  unqualified  term;  and  accord- 
ing to  the  dictum  whatever  may  be  predicated 
of  the  unqualified  term  or  genus  may  be  predi- 
cated of  the  qualified  term  or  species;  or,  in 
other  words,  in  any  universal  proposition  of 
which  the  unqualified  term  is  the  subject,  the 
same  term  qualified  by  an  accident  may  be  legiti- 
mately substituted  for  it;  that  is  to  say,  sym- 
bolically, denoting  by  AY,  Y  as  thus  qualified, 
if  Y  is  X,  then  AY  is  also  X;  as  may  be  thus 
illustrated : 


230  LOGIC 


In  illustration  of  the  supposed  fallacy  (F.  a 
dicto  simpliciter  ad  dictum  secundum  quid]  De 
Morgan  and  others  give  us  the  story  of  the 
stork,  from  Boccaccio,  which,  as  quoted  by 
Professor  Davis,  is  as  follows : 

A  servant  who  was  roasting  a  stork  for  his 
master  was  prevailed  upon  by  his  sweetheart 
to  cut  off  a  leg  for  her  to  eat.  When  the  bird 
came  upon  the  table  the  master  desired  to 
know  what  was  become  of  the  other  leg.  The 
man  answered  that  '  the  stork  never  had  but 
one  leg.'  The  master,  very  angry,  but  deter- 
mined to  strike  his  servant  dumb  before  he 
punished  him,  took  him  the  next  day  into  the 
fields,  where  they  saw  storks  standing  each  on 
one  leg,  as  storks  do.  The  servant  turned 
triumphantly  to  his  master,  upon  which  the  lat- 
ter shouted,  and  the  birds  put  down  their  other 
leg  and  flew  away.  'Ah,  sir,'  said  the  servant, 
but  you  did  not  shout  to  the  stork  at  dinner 
yesterday ;  if  you  had  done  so,  he  would  have 
showed  his  other  leg  too.' 

The  gist  of  which,  the  author  says,  "  is  the 
assumption  that  what  can  be  predicated  of 
storks  in  general  can  be  predicated  of  roasted 


DOCTRINE   OF  FALLACIES  2$  I 

storks, — a  dicto  simpliciter  ad  dictum  secundum 
quid"  But  undoubtedly  (assuming  for  the 
sake  of  the  argument  that  dead  and  roasted 
one-legged  storks  belong  to  the  genus  stork) 
whatever  may  be  universally  predicated  of 
storks  may,  unless  the  dictum  be  a  delusion,  be 
predicated  of  roasted  and  one-legged  storks  as 
well  as  of  others.  The  error,  therefore,  con- 
sists, not  in  an  incorrect  inference  of  the 
particular  proposition  from  the  universal  prop- 
osition including  it,  but  in  the  illicit  assump- 
tion of  the  universal  proposition  that  whenever 
you  shout  at  a  stork  it  will  put  down  a  second 
leg,  though  it  may  have  only  one  leg,  and  be 
dead  and  roasted. 

§  212.  F.  Consequentis. — There  is  much  dis- 
pute as  to  the  nature  of  the  fallacy  intended  by 
Aristotle  under  this  name.  De  Morgan  and 
other  logicians — following  Aldrich — regard  it 
as  consisting  in  the  "  affirmation  of  a  conclu- 
sion "  which  does  not  follow  from  the  premises, 
or,  in  other  words,  as  but  another  name  fora 
Non-scquitur,  which  is  at  least  the  most  con- 
venient view. 

§  213.  CLASSIFICATION  OF  FALLACIES  OF 
THIS  KIND. — According  to  this  view,  the  F. 
Consequentis  will  include  (i)  the  merely  formal 
fallacies,  commonly  known  as  fallacies  of  the 
syllogism ;  and  (2)  all  the  material  fallacies  of 
inference  except  Equivocation.  The  former 


232 


LOGIC 


have  been  sufficiently  treated  in  considering 
the  rules  of  the  syllogism ;  the  latter,  under 
the  head  of  Substitution.  The  former  as  well 
as  the  latter,  and  also  the  fallacies  of  Equivoca- 
tion (or  In  Dictione),  are  also,  it  will  be  remem- 
bered, fallacies  of  Substitution. 


APPENDIX    OF   NOTES 

A-§4 

Perhaps,  when  men  understand  that  the  main 
sources  of  Philosophy  are  to  be  found  in  the 
study  of  words,  we  may  hope  to  escape  the  dreary 
treadmill  on  which  philosophers  have  hitherto  been 
exercising  themselves.  All  progress  in  Philosophy 
that  has  been  made  has  been  the  result  of  the  un- 
conscious observation  of  this  method — as,  e.  g.,  the 
work  of  Locke,  which,  though  weak  in  its  meta- 
physics, constitutes  the  greatest  contribution  to 
philosophy  made  in  modern  times;  and  which,  as 
shown  by  Home  Tooke,  is  merely  an  essay  on  lan- 
guage. "  Perhaps,"  he  says,  "  it  was  for  mankind 
a  lucky  mistake  (for  mistake  it  was)  which  Mr. 
Locke  made  when  he  called  his  book  an  Essay  on 
the  Human  Understanding.  For  some  part  of  the 
inestimable  benefit  of  that  book  has,  merely  on  ac- 
count of  its  title,  reached  to  many  thousands  more 
than,  I  fear,  it  would  have  done  had  he  called  it 
"A  Grammatical  Essay,"  or  "A  Treatise  on 
Words  or  Language  "  {Diversions  of  Pur  ley). 

B— §6 

Comparing  the  physical  sciences  and  the  mathe- 
233 


234  LOGIC 

matics  with  the  moral  sciences,  the  latter  are  infi- 
nitely the  more  difficult  of  achievement;  and  also 
infinitely  more  important  to  the  welfare  of  man- 
kind. For  under  the  name  of  the  moral  sciences 
are  included  all  the  several  branches  of  the 
Science  of  Human  Nature;  which  is  obviously  the 
principal  concern  of  mankind,  and  as  such  the  sci- 
ence to  which  all  others  are  to  be  regarded  as  sub- 
sidiary. This  was  the  distinguishing  characteristic 
of  Socrates'  philosophy.  It  was  expressed  in  the 
injunction  written  over  the  portals  of  the  Delphic 
god:  "  Know  thyself!  "  and  in  modern  times  has 
been  finely  rendered:  "  The  proper  study  of  man- 
kind is  man."  It  is  also  embodied  in  the  fine  old 
term,  the  Humanities,  which  signifies  those  parts  of 
education  that  have  for  their  end  the  development 
of  our  manhood  or  humanity,  and  which  must 
therefore  constitute  the  essential  elements  of  a 
rational  general  education. 


This  was  the  great  discovery  of  Socrates;  to  the 
preaching  of  which,  as  the  gospel  most  needed  by 
men,  his  life  was  devoted.  Nor  have  there  been 
wanting,  in  succeeding  ages,  philosophers  —  and 
those  the  greatest — to  continue  his  mission.  But  so 
averse  are  men  to  being  convinced  of  their  errors 
that  nothing  is  more  odious  to  them  than  the  at- 
tempt. Hence,  generally,  all  means  of  defence  are 
regarded  as  legitimate, — that  is  to  say,  not  only  fal- 
lacies, but  falsehoods  and  slanders,  and,  at  times, 


APPENDIX  OF  NOTES  235 

the  prison,  or  the  rack,  or  death.  Thus  Socrates 
was  poisoned  for  this  offence  only;  which,  though 
otherwise  atrocious,  was  creditable  to  the  Athen- 
ians, as  at  least  proving  an  uncomfortable  mental 
susceptibility  to  the  power  of  reasoning  or  Logic. 
For  in  modern  times  we  have  invented  a  better 
method  of  dealing  with  such  fellows,  and  have 
developed  a  mental  integument  as  impervious  to 
the  weapons  of  reason  as  that  of  the  elephant  or 
rhinoceros  to  the  weapons  of  the  primitive  hunter; 
and  against  which  the  Socratic  wit  would  batter 
in  vain.  Thus  we  are  enabled  to  dispose  of  those 
who  would  disturb  our  mental  peace  and  compla- 
cency, by  simply  refusing  to  listen  to  them,  and  by 
extolling  our  own  idols, — like  the  Ephesians;  who, 
in  answer  to  the  preaching  of  the  apostles,  "all 
with  one  voice,  about  the  space  of  two  hours,  cried 
out:  Great  is  Diana  of  the  Ephesians."  By  these 
two  means  —  which  have  been  aptly  called  "the 
conspiracy  of  silence,"  and  "  the  society  of 
mutual  admiration  " — our  opinions  are  now  im- 
pregnably  buttressed.  Thus  we  live  in  a  sort  of 
Fools'  Paradise  ;  though,  as  Bacon  says,  "  the 
apotheosis  of  error  is  the  greatest  evil  of  all,  and 
when  folly  is  worshipped,  it  is,  as  it  were,  a  plague- 
spot  upon  the  understanding  "  (Nov.  Org.,  bk.  i., 
aph.  Ixv.). 

D— §  it 

The  disuse  of  Logic  must  necessarily  affect  the 
teaching  of  Moral  and  Political  Science,  Metaphys- 
ics, and  the  Science  of  Human  Nature  generally; 


236  LOGIC 

for  the  investigation  of  which  it  is  indispensable. 
Hence,  as  the  proper  study  of  mankind  is  man,  it 
may  be  said  that  the  universities  of  the  day  have 
fallen  behind  their  predecessors  in  efficient  perform- 
ance of  their  most  essential  function.  It  should 
not  be  forgotten  that  the  task  of  reorganizing  Euro- 
pean society  as  it  emerged  from  the  chaos  of  the 
dark  ages  was  mainly  effected  by  such  men  as 
Lanfranco,  Suger,  Anselm,  and  other  churchmen — 
graduates  of  the  mediaeval  schools  and  universi- 
ties, and  consequently  educated  in  Logic  and  Law; 
studies  the  art  of  teaching  which  has  been  lost  by 
our  modern  universities,  and  which  yet  surpass  all 
others  as  means  of  a  rational  education.  That  this 
is  the  case  with  Logic,  it  is  the  aim  of  this  woik  to 
show;  with  regard  to  the  Law,  the  opinion  of  Burke, 
by  those  competent  to  judge,  has  been  generally 
accepted, — that  it  "  is  one  of  the  first  and  noblest 
of  human  sciences  —  a  science  which  does  more  to 
quicken  and  invigorate  the  understanding  than  all 
other  kinds  of  learning  put  together."  Though, 
he  adds,  "it  is  not  apt,  except  in  persons  happily 
born,  to  open  and  liberalize  the  mind  exactly  in 
the  same  proportion." 

E — §  12 

The  peculiar  merit  of  Logic,  as  one  of  the  Hu- 
manities, is  its  perfect  cognoscibility,  and  the 
consequent  facility  with  which  it  can  be  taught. 
Arnauld  in  the  preface  to  the  Port  Royal  Logic 
tells  us  that  he  undertook  to  teach  a  young  noble- 


APPENDIX  OF  NOTES  237 

man  all  that  was  useful  in  Logic  in  four  days,  and 
successfully  performed  the  task.  The  claim  is 
seemingly  extravagant,  but  as  his  notion  of  Logic 
was  confined  mainly  to  the  doctrine  of  the  syllo- 
gism, and  to  so  much  only  of  the  doctrines  of  the 
term  and  of  the  proposition  as  was  incidentally 
necessary,  and  as  the  student  was  a  young  gentle- 
man of  remarkable  ability,  it  may  very  well  be 
credited.  Nor  will  a  more  complete  and  compre- 
hensive study  of  the  subject  add  much  to  the  labor 
of  mastering  it  ;  if  indeed  it  will  not  facilitate  the 
task.  The  general  diffusion  of  logical  culture  can- 
not be  regarded,  therefore,  as  a  vain  aspiration. 
The  subject  requires  no  preliminary  culture  other 
than  the  studies  usually  taught  in  the  common 
schools,  and  may  be  readily  mastered  by  almost 
any  young  man  of  average  ability  and  the  proper 
age — say  sixteen  or  seventeen.  And  this  will  espe- 
cially be  the  case  with  one  who  has  thoroughly 
mastered  the  elements  of  algebra  and  geometry. 
Thus  it  is  quite  possible  to  devise  a  very  brief 
course  of  study  sufficiently  thorough  to  train  the 
student  as  a  reasoning  creature,  and  to  make  him 
equally  competent  with  the  graduates  of  our  great 
universities  to  grapple  with  all  the  great  problems 
of  Politics  and  Morality;  and,  indeed,  until  our 
modern  university  education  be  reformed,  even 
more  so.  This  was  illustrated  by  the  mediaeval 
universities,  to  whose  graduates,  as  we  have  ob- 
served, the  reorganization  of  society  at  the  close  of 
the  dark  ages  was  entrusted,  and  by  whom  the 
task  was  successfully  accomplished;  nor  do  I  think 


238  LOGIC 

it  extravagant  to  say  that  alongside  of  them  in  prac- 
tical politics  our  modern  graduates  would  be  but 
children.  Of  the  subjects  taught  outside  of  The- 
ology the  principal,  as  we  have  said,  were  Logic  and 
Law,  and  these  must  be  regarded  as  the  most  essen- 
tial parts  of  a  rational  education.  The  latter  will 
require  long  and  persevering  study,  but  a  thorough 
logical  training  will  render  the  student  competent 
to  master  it;  and  without  such  training  —  either 
systematically  taught  to  him  at  the  outset,  or  grad- 
ually acquired  in  the  study  of  the  law  itself  —  its 
mastery  is  impracticable  ;  and  the  same  observation 
is  true  with  reference  to  Political  Science  generally. 


I  have  been  admonished  by  a  friend  that  the  use 
of  examples  of  this  kind  in  an  elementary  work 
may  be  hazardous;  and  this,  I  understand,  on  the 
double  ground  that  the  younger  student  may  find 
it  difficult  to  understand  them  and  the  older,  regard 
them  as  disputable;  and  that  thus  they  must  prove 
to  the  one  a  stumbling-block,  and  to  the  other  fool- 
ishness. With  regard  to  the  last  objection,  it  is  to 
be  admitted  that  if  any  of  the  examples  are  in  fact 
disputable,  the  objection  is  well  taken.  But  I  am 
persuaded  that,  if  they  appear  so  to  any  one,  it  is 
only  because  of  the  universal  bias  of  men  in  these 
unlogical  times  in  favor  of  their  opinions,  and  that 
any  one  who  will  provisionally  reject  all  prejudice 
will  see  at  once  that  the  argument  is  in  every  case 
demonstrative.  Or  if  in  any  case  I  am  deceived, 


APPENDIX  OF  NOTES  239 

then  my  own  reasoning  will  serve  for  example. 
With  regard  to  the  younger  student,  the  opinion 
seems  to  be  that  it  would  be  better  to  illustrate 
the  nature  of  the  fallacies  by  the  more  familiar 
examples  of  the  character  commonly  used  in  the 
current  logics.  But  this,  I  think,  to  be  a  great 
mistake.  The  fallacies  are  themselves  sufficiently 
simple  to  be  readily  understood,  and  trivial 
examples  merely  serve  to  lead  the  student  to 
suppose  that  he  is  in  no  danger  of  falling  into 
them.  I  have  therefore  thought  it  far  better  to 
take  my  examples  from  theories  that  have  played 
and  are  now  playing  a  great  part  on  the  stage  of 
history.  Nor  are  these,  when  treated  logically,  at 
all  difficult,  with  a  little  reflection,  to  understand; 
and  indeed  it  is  to  be  assumed  that,  if  a  young  man 
has  arrived  at  the  age  at  which  he  can  study  Logic 
profitably  without  some  familiarity  with  these  ques- 
tions, his  education  has  been  much  neglected. 
Neither  this  nor  any  part  of  my  work  can,  indeed, 
be  understood  without  the  independent  thought  of 
the  reader;  but  this  also  I  consider  not  only  a  great 
advantage,  but  an  essential  condition  to  the  right 
exposition  of  the  subject.  For  though  the  princi- 
ples of  Logic  are  extremely  definite,  and  therefore 
readily  cognoscible,  yet,  as  already  observed,  they 
require  for  their  mastery  the  same  kind  and  degree 
of  study  as  is  required  by  the  mathematics;  and 
there  is  no  royal  road  to  Logic  any  more  than  to 
geometry.  If  the  student,  therefore,  will  take  the 
trouble  to  work  out  thoroughly  these  examples,  and 
others  of  the  same  character  (of  which  many  will 


240  LOGIC 

suggest  themselves),  he  will  achieve  not  only  a 
mastery  of  the  principles  involved  in  them,  and  of 
the  practical  use  of  Logic,  that  cannot  be  otherwise 
attained,  but  also  an  accurate,  though  limited, 
knowledge  of  all  the  great  political,  social,  and 
moral  questions  involving  the  welfare  of  mankind; 
which,  better  than  anything  else,  will  serve  as 
an  introduction  to  those  studies.  I  have  also, 
in  the  use  of  these  examples,  another  point  in 
view,  which  is,  that,  by  means  of  the  application 
of  logical  principles,  these  apparently  difficult 
problems  are  readily  solved,  and  the  most  im- 
portant heresies  in  Politics  and  Morality  that 
afflict  mankind  exposed;  and  thus  are  proved,  by 
practical  illustration,  the  theses  with  which  I  com- 
menced,—  that  in  all  the  moral  sciences  the  use  of 
Logic  is  essential,  and  that  the  confused  and  un- 
satisfactory condition  of  the  literature  of  these 
subjects  is  due  to  the  decay  of  Logic. 

In  conclusion,  however,  I  would  say  that  while 
regarding  the  current  examples  used  in  the  logics 
as  inadequate  for  the  illustration  of  the  subject,  I 
have  not  neglected  them,  but,  in  the  chapter  on 
the  Traditional  Doctrine  of  Fallacies,  have  con- 
fined myself  mainly  to  them. 

G— §  14 

This  is  strenuously  objected  to  by  Hamilton. 
"  Dr.  Whately, "  he  says,  "  is  contradictory.  .  .  . 
In  some  places  he  makes  the  operation  of  reasoning 
not  only  the  principal,  but  the  adequate  object  of 


APPENDIX  OF  NOTES  241 

Logic.  ...  In  others,  he  makes  this  total  or 
adequate  object  to  be  the  language.  But  as  there 
cannot  be  two  adequate  objects,  and  as  language 
and  the  operation  of  reasoning  are  not  the  same, 
there  is  therefore  a  contradiction  "  (Logic,  u). 

But  though  language  and  reasoning  are  not  the 
same,  yet  they  are  the  same  so  far  forth  as  Logic 
is  concerned  with  either;  for,  as  Logic  has  to  deal 
only  with  reasoning  expressed  in  language,  it  is 
necessarily  concerned  with  both  to  the  same  extent; 
and  we  may  say,  with  equal  propriety,  that  the 
subject-matter  of  Logic  is  either  language  or 
reasoning. 

The  error  of  Hamilton  lies  in  the  illicit  assump- 
tion that  the  term  "  language  "  is  equivalent  to  the 
external  logos,  i.  e.,  the  expression,  as  opposed  to 
the  inward  thought.  But  if  language  be  construed 
as  denoting  both  the  thought  and  the  expression,  as 
it  should  be,  the  only  objection  disappears;  and 
when  thus  construed,  the  proposition  that  Logic  is 
concerned  wholly  with  language  is  too  clear  to  be 
disputed. 

H— §  1 6 

The  name  given  to  the  subject  by  Aristotle  was 
the  "  Analytics."  The  name  Logic  seems  to 
have  been  first  applied  to  it  in  the  time  of  Zeno, 
the  Stoic.  Many  names  have  been  invented  to  sig- 
nify the  scope  of  Logic, — as,  e.  g.,  the  Architectonic 
Art;  the  Organon,  or  Instrument;  the  Ars  Artium, 
or  Disciplina  Disciplinarum;  Heuristic,  or  the  Art 
of  Discovering  Truth;  the  Medicina  Mentis,  or  the 

16 


242  LOGIC 

Cathartic  of  the  Mind,  etc.  (Thompson,  Laws  of 
Thought,  §35);  and  to  these  should  be  added  the 
name  given  by  Socrates  to  his  own  doctrine  (which, 
though  the  fact  is  commonly  overlooked,  was  noth- 
ing else  than  Logic),  namely,  the  Obstetrics  of  the 
Mind  (Maieusis), 

Of  these,  the  last  two  names  express  precisely 
the  two  main  functions  of  Logic,  — that  is  to  say, 
ist,  to  serve  as  a  cathartic  of  the  mind  to  rid  it  of 
the  false  persuasion  of  knowledge;  for,  as  has  been 
well  said,  "  the  natural  state  of  the  human  mind  " 
is  "  not  simply  ignorance,  but  ignorance  mistaking 
itself  for  knowledge  "  (Grote's  Plato,  i.,  p.  373)  ; 
and,  2d,  to  bring  forth  from  the  mind  "  answers  of 
which  it  is  pregnant"  (Id.,  p.  367);  or,  in  plain 
language,  to  develop  and  formulate  the  unformed 
ideas  in  our  minds,  whether  innate  or  acquired 
from  without.  See  Socrates'  own  account  of  this 
function,  as  given  in  the  Thesetetus  (Id.,  iii.,  p. 
112). 

I-§37 

There  is  much  confusion  with  modern  logicians 
with  regard  to  the  nature  of  first  and  second  inten- 
tions or  notions,  but  the  above  definition  seems  to 
accord  with  the  best  authorities  and  expresses  a 
distinction  of  fundamental  importance.  According 
to  this  definition,  Notions  of  Second  Intention 
will  include  all  abstract  notions,  and  also  notions  of 
classes  of  real  individuals  construed  collectively; 
in  which  case  they  become  abstract. 

The  following  is  the  definition  of  Aquinas  (Opus- 


APPENDIX  OF  NOTES  243 

cula,  cited  Krauth,  Voc.  of  Phil.  Art.,  "  Intention, 
First  and  Second  "): 

"  Nouns  of  first  intention  are  those  which  are 
imposed  upon  things  as  such,  that  conception  alone 
intervening  by  which  the  mind  is  carried  imme- 
diately to  the  thing  itself.  Such  are  man  and 
stone.  But  nouns  of  the  second  intention  are  those 
which  are  imposed  upon  things  not  in  virtue  of 
what  they  are  in  themselves,  but  by  virtue  of  their 
being  subject  to  the  intention  which  the  mind 
makes  concerning  them,  as  when  we  say  that  man 
is  a  species  and  animal  a  genus."  Which  seems  to 
accord  with  our  definition  :  that  is  to  say,  if  we 
speak  of  man  as  denoting  the  class  of  individual 
men,  the  name  is  of  the  first  intention,  but  if  we 
regard  man  collectively  as  a  significate  of  the  class 
animal,  the  name  is  of  second  intention;  and  so 
with  reference  to  all  other  abstract  names.  Names 
of  second  intention  are  precisely  denoted  by  the 
term  "  univer sales  a  parte  ret," — /.  e.,  universal 
notions  considered  apart  from  things,  or,  in  other 
words,  abstract  notions, —  and  also  by  the  term 
"  beings  of  reason,"  as  quoted  infra. 

The  division  of  names  into  names  of  first  and  of 
second  intention  was  obviously  intended  to  com- 
prehend all  names;  and  hence,  if  names  of  first 
intention  are  identical  with  concrete  names, — as  they 
evidently  are, —  names  of  second  intention  must  in- 
clude all  abstract  names;  and  it  is  not  admissible 
to  confine  them  (as  Mansel  does)  to  some  of  that 
class  only.  Accordingly  a  universal  (ens  unum 
in  multis]  is  defined  by  Aldrich  simply  as  a 


244  LOGIC 

predicable, —  /.  e. ,  as  "Nomen  Commune,  Univocum, 
Secundce  Intentionis,  uno  verbo,  Predicabilis,  Sive 
Vox  apta  prcedicare,  i.  e. ,  Univoce  did  de  multis ' ' 
(Aid.  Log.,  p.  23). 

It  is  singular  that  in  the  Port  Royal  Logic  this 
distinction  should  be  regarded  as  unimportant,  and 
even  made  the  subject  of  ridicule.  "  No  one, 
thank  God!  "  it  is  said,  "  now  takes  any  interest  in 
'  the  universal  a parte  rei,'  or  '  beings  of  reason,'  or 
in  '  second  intentions.'  Thus,  there  is  no  ground 
to  apprehend  that  any  one  will  be  offended  at  our 
having  said  nothing  about  them."  But  it  may  be 
safely  said  that  no  one  can  have  an  adequate  con- 
ception, either  of  the  nature  or  use  of  Logic,  until 
the  notion  expressed  in  the  term  "  second  inten- 
tions," and  the  other  phrases  cited  (which  are 
similar  in  meaning),  are  thoroughly  grasped. 

K-§38 

Even  where  we  use  concrete  terms,  it  is  not  the 
thing  itself,  but  the  notion  of  the  thing  that  is  pres- 
ent to  the  mind.  For,  as  is  said  by  Hobbes, 
"  seeing  names  ordered  in  speech  (as  is  defined) 
are  signs  of  our  conceptions,  it  is  manifest  they  are 
not  the  signs  of  the  things  themselves."  Hence, 
as  Mansel  says,  "  concepts  (or  notions]  are  the  things 
of  Logic."  On  this  point  Max  Miiller's  Laws  of 
Thought  (the  opening  chapters)  may  be  read  with 
profit.  For  without  acceding  altogether  to  his  the- 
ory,—  that  thought  is  impossible  without  language, 
—  this  is  certainly  true  (ex  vi termini),  as  to  ratioci- 
nation, or  explicit  reasoning,  and  may  therefore  be 
accepted  without  error,  and  much  to  his  profit,  by 


APPENDIX  OF  NOTES  245 

the  logician.  According  to  Home  Tooke  "  thing  " 
and  "  think  "  are  but  the  same  word  spelt  differ- 
ently; and  hence,  he  says,  "  the  vulgar  pronuncia- 
tion of  '  nothink  '  instead  of  '  nothing '  is  not  so 
very  absurd." 

L-§53 
BOOLE'S  LOGIC 

"  All  the  operations  of  language,  as  an  instru- 
ment of  reasoning,  may,"  it  is  claimed  by  Mr. 
Boole,  "  be  conducted  by  a  system  of  signs  com- 
posed of  the  following  elements,"  viz. : 

ist.  "  Literal  symbols,  as  x,  y,"  etc.,  represent- 
ing names  or  terms. 

2d.  "  Signs,  as  -|-,  — ,  X,"  representing  relations 
to  each  other  of  the  substantive  elements  of  com- 
plex terms. 

3d.  "  The  sign  of  identity  (  =  ),"  or,  as  I  should 
call  it,  the  sign  of  equivalence,  /.  e.,  of  significative 
equivalence,  or  equivalence  of  denotation. 

The  names  signified  by  signs  of  the  first  class 
may  be  either  single  names  denoting  classes, — as, 
e.  g.,  man,  horse,  good,  white,  etc., —  or  they  may 
be  composed  of  several  names,  denoting  classes 
that  partially  coincide  —  as,  e.  g.,  good  men,  black 
sheep,  etc.  In  the  latter  case  the  signs  may  be 
combined  together  precisely  as  the  words  denoting 
the  terms.  Thus,  if  we  represent  the  class  men 
by  x,  and  the  class  good  by  y,  "  good  men  "  will 
be  denoted  by  the  expression  yx.  So  if  x  stands 
for  sheep,  y  for  black  things,  and  z  for  horned  things, 
zyx  will  denote  "  horned  black  sheep."  But  it  is 
obvious  that  in  the  expression  "  black  sheep,"  the 


246  LOGIC 

order  in  which  the  component  terms  are  placed 
makes  no  difference  ;  or,  in  other  words,  that  it  is 
the  same  thing  whether  we  say  "  black  sheep"  as  in 
English,  or  "  sheep  black"  as  in  Spanish  and  other 
languages.  Consequently,  the  class  "  black  sheep  " 
may  be  written  either  yx  or  xy,  which  may  be  ex- 
pressed by  the  following  equation: 


(i)yx  =  xy. 


In  which  the  complex  term  yx  or  xy  denotes  a 
class  of  individuals  that  is  at  once  included  in  the 
class  7  and  the  class  x.  On  the  same  principle,  if 
we  represent  by  z  the  adjective  "  horned,"  zyx  will 
stand  for  the  term  "horned  black  sheep"  and  we 
will  have  the  following  equations: 


(2)  zxy  =  xyz  =  yxz. 


If,  in  the  equation  xy  =  yx,  we  suppose  y  to  be 
wholly  included  in  x, — as,  e.  g.,  if  it  denote  the 
black  sheep  in  the  flock  x, — then  we  will  have  the 
equation : 


(3)  xy  =  y. 
Again,  if  x  =  y,  then  xy  =xa.     But  a  class  is  not 


APPENDIX  NOTES  247 

enlarged  or  diminished  by  repeating  the  term  de- 
noting it.  Thus,  "  white  white  "  or  "sheep  sheep  " 
mean  nothing  more  than  "white"  or  "sheep." 
Hence  we  have  the  equation: 

(4)   x'  =  x. 

If  the  class  denoted  by  a  term  is  composed  of 
two  classes,  denoted  respectively  by  x  and  y,  as, 
e.g.,  "  men  and  women,"  it  may  be  expressed  by 
the  complex  term  x  +  y.  But  obviously,  the  ex- 
pressions, "  men  and  women,"  and  "  women  and 
men,"  are  equivalent  in  meaning.  Hence  the 
equation: 

(5)  x  +  y  =  y  +  x. 

Again,  if  we  qualify  the  term  ' '  men  and  women  ' ' 
by  the  adjective  "Asiatic,"  we  have  the  expres- 
sion "Asiatic  men  and  women  ";  but  this  is  equiv- 
alent in  meaning  to  the  expression  "  Asiatic  men 
and  Asiatic  women."  Hence,  denoting  men  by  x, 
women  by  y,  and  Asiatic  by  z,  we  have  the  equation : 

(6)   z(x  +  y)  =  zx  +  zy. 

If  we  denote  the  adult  population  of  a  city  by  x, 
and  the  women  by  y,  then  x  —  y  will  denote  the 
men.  But  it  is  indifferent  whether  we  express  the 
excepted  class  first  or  last,  provided  it  be  distinctly 
represented  as  the  exception.  Thus  the  expres- 
sion, "  the  adult  population  less  the  women,"  and 
the  expression,  "excepting  the  women,  the  adult 


248  LOGIC 

population,"  are  equivalent  in  meaning  to  each 
other,  and  botli  to  the  expression  "  the  men." 
Hence  we  have  the  equation: 

(7)  x  -  y  =  -  y  +  x. 

But  the  expression,  "  the  white  population,  less 
the  women,"  is  equivalent  in  meaning  to  the  ex- 
pression, "  the  white  population,  less  the  white 
women." 

Hence,  representing  "  while  "  by  z,  we  have  the 
equation: 

(8)  z  (x  —  y)  =  zx  — zy. 

If,  in  the  proposition,  "  The  stars  are  the  suns 
and  the  planets,"  we  denote  stars  by  x,  suns  by  y, 
and  planets  by  z,  we  shall  have  the  equation : 

(9)  x  =  y  +  z. 

But,  if  the  stars  are  the  suns  and  the  planets,  the 
stars,  except  the  planets,  are  suns.  Hence  we  have 
the  equation: 

(10)  x  —  z  =  y. 

If  the  terms  x  and  y  are  equivalent,  it  is  obvious 
that  those  of  the  class  x,  or,  as  we  may  say,  the  x's, 
that  possess  a  given  quality,  must  be  identical  with 
the  y's  that  possess  it.  Hence,  if  x  =  y,  we  have 
the  equation: 

(n)  zx  =  zy. 


APPENDIX  NOTES  249 

But,  per  contra,  it  cannot  be  inferred  from  the 
equation,  zx  =  zy,  that  x  =  y.  (§  82  (2)  n.) 

For,  "  suppose  it  true  that  those  members  of  a 
class  x  which  possess  a  certain  quality,  z,  are  iden- 
tical with  those  members  of  a  class  y,  which  possess 
the  same  quality,  z,  it  does  not  follow  that  the 
members  of  the  class  x  universally  are  identical 
with  the  members  of  the  class  y."  Thus,  return- 
ing to  our  sheep,  let  x  denote  one  portion  of  a 
flock  of  sheep,  and  y  another,  and  let  z  denote 
"horned"  ;  then  zx  will  denote  the  horned  sheep 
in  one  portion  of  the  flock,  and  zy  the  horned  sheep 
in  the  other;  and,  if  we  suppose  these  to  be  equal, 
we  shall  have  the  equation: 

zx  =  zy. 

But  it  will  not  follow  that  the  two  portions  of  the 
flock  are  equal  in  number,  and  we  therefore  can- 
not say  x  —  y  ;  as  may  be  thus  illustrated  : 


Adverting  to  the  above  equations,  it  will  be  per- 
ceived that  the  laws  governing  the  convertibility  of 
the  different  forms  of  expression  are,  to  a  certain 
extent,  identical  with  those  obtaining  in  mathe- 
matics. Thus,  in  the  equations  (i)  and  (2),  the 
symbols  are  commutative  like  the  symbols  of  algebra. 
The  logical  process  here  involved  is,  therefore, 
expressed  in  the  same  manner  as  in  the  correspond- 


250  LOGIC 

ing  algebraic  expression  ;  and  this  expression, 
whether  regarded  as  logical  or  algebraic,  will  be 
subject  to  the  same  law.  There  is,  therefore,  in 
the  process  involved  in  these  equations,  (i)  and  (2), 
a  certain  resemblance  or  analogy  to  the  process  of 
multiplication;  and  this  is  also  true  of  equation 

("). 

In  equations  (6)  and  (8)  a  process  is  exhibited 
closely  resembling  that  of  factoring  in  algebra. 

In  equations  (5),  (7),  (9),  and  (10),  we  have 
illustrated  a  principle  of  conversion  of  symbols 
apparently  identical  with  the  corresponding  process 
in  algebra.  Hence  we  may  affirm  as  logical  axioms: 
ist,  that  if  equals  be  added  to  equals  the  wholes 
will  be  equal;  and,  2d,  that  if  equals  be  taken  from 
equals,  the  remainders  will  be  equals. 

Hence,  with  regard  to  the  equations  specified 
(i,  2,  u,  6,  8,  5,  7,  9,  and  10),  we  may  affirm  gen- 
erally that  the  logical  symbols  may  be  transposed 
or  converted  precisely  in  the  same  way  as  in  the 
operations  of  addition,  subtraction,  and  multiplica- 
tion in  algebra.  But  with  regard  to  the  analogy 
between  multiplication  and  the  corresponding 
logical  operation,  it  will  be  observed  that  in  one 
respect  it  fails,  namely,  in  equation  (4),  x2  =  x; 
which  is  good  in  Logic,  but  not  generally  true  in 
algebra.  Also,  it  will  be  observed,  there  is  appa- 
rently no  logical  process  corresponding  to  the  alge- 
braic operation  of  division.  Thus,  as  we  have 
seen,  we  cannot  infer  from  equation  (n),  "  zx  = 
zy, "  that  x  =  y,  as  we  may  in  algebra. 

But  if  we  conceive  of  an  algebra  or  arithmetic 


APPENDIX  NOTES  251 

that  deals  only  with  the  two  numbers,  i  and  o,  this 
discrepancy  will  altogether  disappear.  For  on  such 
hypothesis,  equation  (4),  x2  =  x,  will  be  true,  both 
in  Logic  and  in  mathematics.  And  in  equation 
(u),  zx  =  zy,  if  z  =  i,  the  proposition,  x  =  y, 
may  be  inferred,  both  in  Logic  and  in  mathe- 
matics. But  if  z  be  equal  to  zero,  it  cannot  be 
thus  inferred,  either  in  Logic  or  algebra.  Hence, 
if  we  conceive  of  an  algebra  in  which  the  symbols 
x,  y,  z,  etc.,  "  admit  indifferently  of  the  values  of 
i  and  o  and  of  those  values  alone,"  then  "  the  laws, 
the  axioms,  and  the  processes  of  such  an  algebra 
will  be  identical  in  their  whole  extent  with  the  laws, 
axioms,  and  process  of  an  algebra  of  Logic." 

Accordingly,  Mr.  Boole's  system  is  founded  on 
this  hypothesis,  and  "  the  logical  value  and  signifi- 
cance "  of  the  terms  dealt  with  (i  and  o)  are  thus 
explained.  In  algebra,  the  equation  oy  =  o  is  true, 
whatever  the  value  of  y.  So,  in  Logic,  if  o  be  re- 
garded as  a  class,  whatever  class  may  be  denoted 
by  y,  the  equation  oy  =  o  will  be  true;  for,  as  we 
have  seen,  oy  denotes  the  class  of  individuals  that 
are  at  the  same  time  included  in  the  two  classes, — 
/'.  e.,  o  and  y.  But  none  are  included  in  the  class 
o,  and  therefore,  oy  =  o. 

So  in  algebra,  the  equation  ly  =  y  is  true,  what- 
ever the  value  of  y  may  be,  and  this  is  true  in  Logic 
also,  if  i  be  regarded  as  including  y.  For  as  we  have 
seen  (equation  3),  if  one  of  the  two  terms  making  a 
combined  term  is  included  in  the  other,  the  com- 
bined term  is  equal  to  the  term  of  least  extension. 
But  this  condition  may  be  satisfied  by  regarding  i 


252  LOGIC 

as  denoting  the  Universe.  "  Hence,  the  respective 
interpretations  of  the  symbols,  o  and  i,  in  the  sys- 
tem of  Logic,  are  Nothing  and  Universe. ' '  Denoting 
the  Universe  by  i,  and  men  by  x,  the  expression 
i  —x  denotes  the  class  "  not-men," — /.  e.,  all 
animals  that  are  not  men. 

The  equation  x2  =  x  may  be  put  in  the  form, 
x"  —  x  =  o,  and  this  again  in  the  form,  x  (i  —  x) 
=  o;  of  which  the  interpretation  is  obvious;  for, 
if  x  denotes  "  men,"  and  i  —  x  "  not-men,"  it  is 
clear  that  there  can  be  no  individuals  belonging  at 
once  to  the  two  classes,  x  and  i  —  x,  or,  men  and 
not-men.  So  if  we  denote  by  x  any  class  charac- 
terized by  the  possession  of  any  quality  whatever 
the  same  result  will  follow. 

It  is  observed  by  Mr.  Boole  that  the  principle  of 
analysis  and  classification  involved  in  his  system  is 
"  division  into  pairs  of  opposites,  or,  as  it  is  techni- 
cally said,  Dichotomy  "  (§  47),  and  this  is  in  fact  the 
fundamental  process  in  Logic.  And  this,  it  will 
be  observed,  agrees  with  the  opinion  of  Hobbes 
and  of  Aristotle  (§  90  n.). 

In  equation  (5),  it  will  be  observed,  there  is  a 
certain  ambiguity  in  the  expression  x  -)-  y.  In 
common  speech  the  classes  denoted  by  the  sym- 
bols x  and  y  may  either  be  exclusive  of  each 
other,  or  they  may  overlap,  as,  for  instance,  in  the 
proposition,  "  Scholars  and  men  of  the  world  de- 
sire happiness,"  or,  "  Useful  things  are  those  that 
either  produce  pleasure,  or  prevent  pain."  In 
Mr.  Boole's  system  this  ambiguity  is  removed. 

If  the  two  classes  are  intended  to  include  each 


APPENDIX  NOTES  253 

other,  the  expression  to  denote  the  aggregate  class 
will  bex(i  —  y)  +  y(I  —  x);  which  is  to  be  read 
x's  that  are  not  y's,-  and  y's  that  are  not  x's. 

If  we  intend  two  classes  that  overlap,  then  the 
full  expression  should  be,  xy  +  x  (i  — y)  -j-  y  (i  — x). 

"  The  result  of  these  investigations  may  be  em- 
bodied in  the  following  rule  of  expression: 

"  RULE. — Express  simple  names  or  qualities  by 
the  symbols  x,  y,  z,  etc.,  their  contraries  by  i  —  x, 
i  —  z,  etc. ;  classes  of  things  defined  by  common 
names  or  qualities,  by  connecting  the  correspond- 
ing symbols  as  in  multiplication;  collections  of 
things  consisting  of  portions  different  from  each 
other,  by  connecting  the  expressions  of  those  por- 
tions by  the  sign  +.  In  particular,  let  the  expres- 
sion, '  Either  x's  or  y's  '  be  expressed  by  x 
(i—  y)  +  y  (i  —  x)  when  the  classes  denoted  by 
x  and  y  are  exclusive;  by  x  -[-  y  (i  —  x)  when  they 
are  not  exclusive.  Similarly  let  the  expression, 
'  Either  x  's  or  y's  or  z's  '  be  expressed  by  x 
(i  -  y)  (i  -  z)  +  y  (i  -  x)  (i  -  z)  +  z  (i  -  x) 
(i  —  y),  when  the  classes  denoted  by  x,  y,  and 
z  are  designed  to  be  mutually  exclusive;  and  by 
x  +  y  (i  —  z  )+  z  (i  —  x)  (i  —  y),  when  they  are 
not  meant  to  be  exclusive,  and  so  on." 

For  illustration,  "  let  us  assume 

x  —  hard,  y  =  elastic,  z  =  metals; 

and  we  shall  have  the  following  results: 

"  '  Non-elastic    metals  '  will    be    expressed   by 

zO  -  y); 


254  LOGIC 

'  Elastic  substances  with  non-elastic  metals  '  by 
y  +  z(i  -  y); 

'  Hard  substances,  except  metals,'  by  x  —  y; 
"  '  Metallic   substances,  except  those  which  are 
neither  hard  nor  elastic,'  by  z  —  z  (i  —  x)  (i  —  y), 
or  by  z[i  -  (i  -  x)  (i  -y)]." 

The  above  brief  account  of  the  elements  of  Mr. 
Boole's  system  is  given  for  the  purpose  of  illus- 
trating the  laws  that  govern  the  convertibility  of 
terms,  and  of  substantive  elements  of  terms;  or,  in 
other  words,  that  govern  the  formal  substitution  of 
equivalent  expressions,  (§  67  (2)) — a  purpose  for 
which  it  admirably  serves.  It  will  require  some 
attention  to  understand  it,  but  with  such  attention, 
no  difficulty  will  present  itself. 

It  may  be  readily  perceived  that  by  the  use  of 
fhe  above  data  a  very  extensive  calculus  may  be 
developed,  and  such  a  one  has  in  fact  been  devel- 
oped by  Mr.  Boole;  but  with  regard  to  its  utility, 
opinions  may  widely  differ. 

'  The  idea  of  a  logical  calculus,"  says  Lotze, 
"has  been  often  taken  up  and  often  abandoned; 
but  the  Englishman  Boole  has  recently  made  an 
elaborate  and  careful  attempt  to  carry  it  out,  which 
is  beginning  to  attract  attention  in  Germany,  as 
well  as  in  his  own  country.  Though  I  freely 
admit  that  the  author's  ingenuity  makes  his  able 
work  very  charming,  I  am  unable  to  convince  my- 
self that  this  calculus  will  help  us  to  solve  problems 
which  defy  the  ordinary  methods  of  Logic." 
(Logic,  vol.  ii.,  277.) 


APPENDIX  NOTES 

M— §96 

TABLE  OF  SYLLOGISMS 


255 


rYX 

ist  Figure  •<  ZY 
(  ZX 

A: 

Barbara 
V  is  X             S^i 

v\ 

A: 

z  is  Y       nf^ 

A: 

.'.ZisX           V_ 

JJ 

E: 

Celarent 

Y  is  not  X        / 
Is  — 

\'     \ 

A: 

Z  is          Y     ((  z 

E: 

Y"" 

.'.  Z  is  not  X        >  — 

-S 

Darii 

Ferio 

A: 
I: 

Y  is  X                  / 
Some  Z  is  Y    I    t 

^~X**\      E:       Y  is  not  X              ^_^^ 
^T\l     I:         Some  Z  is  Y           \_//v\  *  J 

I: 

\ 

.'.  Some  Z  is  X 

V.5/     O:  .'.  Some  Z  is  not  X          ^»  —  * 

rXY 

^</  Ft  git  re  •<  ZY 
(ZX 

Cesare 

Cif/iS^M/ 

E: 
A: 
E: 

X  is  not  Y 
Z  is          Y 
.'.  Z  is  not  X 

x  ^                                   E:       Y  is  not  X 

(0Y)  0 

V*'     J                                E:  .'.  Z  is  not  X 

256 


LOGIC 


Came  sir  es 

Celarcnt 

A: 

X  is  Y 

E: 

Y  is  not  Z 

E: 
E:  . 

Z  is  not  Y 
'.  Z  is  not  X 

© 

A: 
E: 

X  is  Y 
.'.  X  is  not  Z 

or  Z  is  not  X 

Festino 

E:  XisnotY 

I:         Some  Z  is         Y 

O:  .'.  Some  Z  is  not  X 

Fakoro 
A:  X  is         Y 

O:       Some  Z  is  not  Y 
O:  .'.  Some  Z  is  not  X 


Ferio 

E:  YisnotX 

I:         Some  Z  is         Y 

O:  .'.  Some  Z  is  not  X 

Ferio 
E:          Not-Y  is  not  X 

I:         Some  Z  is  not  Y 
O:  .'.  Some  Z  is  not  X 


rYX 

jd  Figure  -j  YZ 

(zx 

Darapti 

Darii 

A: 

YisX                 /^~~/*\^\ 

A: 

Y 

isX 

A: 

YisZ                  (z    /(7)J   x  J 

I: 

Some  Z 

isY 

I: 

.'.SomeZisX                  Vj^Lx 

I: 

.'.  Some  Z 

isX 

Disamis 

Darii 

I: 

Some  Y  is  X                     /•     ^N, 

A: 

Y 

is  Z 

A: 

Y  is  Z                  /f>  /jX 

I: 

Some  X 

is  Y 

I: 

.-.  SomeZisX                  \S-K    /  X    ) 

I: 

.'.  Some  X 

is  Z 

^V  y 

or  Some  Z 

isX 

APPENDIX  NOTES 

257 

Datisi 

Darii 

A: 

Y  isX               /^S^^rx 

A:                  Y  is  X 

/(     Y    /)     \2\ 

I: 

Some  Y  is  Z                    (  V_J()/ 

I:         Some  Z  is  Y 

\        X        y' 

I: 

.'.  Some  Z  is  X                     ^~-^*/ 

I:    .'.  Some  Z  is  X 

Felapton 

Ferio 

E: 

Y  is  not  X           /^£~^><  —  ~x             K: 

Y  is  not  X 

A: 

Yis           Z          O(      )  X]          I: 

Some  Z  is         Y 

O: 

.  '.  Some  Z  is  not  X           ^~_3<^       >/         O: 

.'.  Some  Z  is  not  X 

Dokamo 

Darii 

O: 

Some  Y  is  not  X             /  ^^                   A: 

YisZ 

A: 

Yis          Z          [CyQ)x\        ^ 

Some  not  —  X  is  Y 

Some  not  —  X  is  Z 

O: 

.'.  Some  Z  is  not  X            \^2^^                or 

Some  Z  is  not  —  X 

Ferison 

Ferio 

E: 

Y  is  not  X                /'TN  /—  \              E: 

Y  is  not  X 

(  *  JL-L  x  i 

I: 

Some  Yis          Z               V^Vy              I: 

Some  Z  is          Y 

O: 

.'.  Some  Z  is  not  X                    ^—  /                   O: 

.'.  Some  Z  is  not  X 

/XY 

4th  Figure  -|  YZ 

(zx 

Bramantip 

Barbara 

A: 

Xis  Y                      /""""X 

A:                  Y  is  Z 

A: 

Y  is  z        /fer\  \ 

A:                  X  is  Y 

I: 

.'.  Some  Z  is  X                     \&jj 

A:  .'.             X  is  Z 

v^_/ 

or  Some  Z  is  X 

Camenes 

Celarent 

A: 

X  is         Y                   /TX 

E:        Y  is  net  Z 

E: 
O: 

Y  is  not  Z                   /V"  X    \       x"~x 

.-.  z  is  not  x            \v  x  y  /    (  z  y 

A:        X  is         Y 
E:  .'.  X  is  not  Z 
or  Z  is  not  X 

258 


LOGIC 


Dimaris 

I :         Some  X  is  Y 
A:  Y  is  Z 

I:    .'.  Some  Z  is  X 

Fesapo 

E:  XisnotY 

A:  Y  is          Z 

I:    .'.  Some  Z  is  not  X 

Fresison 

X  is  not  Y 
Some  Y  is          Z 
O:  .'.  Some  Z  is  not  X 


Darii 

A:  Y  is  Z 

I:         Some  X  is  Y 
I:    .'.  Some  X  is  Z 
or  Some  Z  is  X 

Ferio 

Y  is  not  X 
Some  Z  is         Y 
O:  .'.  Some  Z  is  not  X 

Ferio 

E:  Y  is  not  X 

I:         Some  Z  is          Y 
O:  .'.  Some  Z  is  not  X 


N — §  no 

The  opinion  of  Locke  cited,  which  occurs  at  the 
end  of  his  essay,  may  be  taken  as  the  consumma- 
tion and  final  generalization  of  his  theory  of  knowl- 
edge. In  the  body  of  the  work  the  conclusion 
reached  by  him  is,  that  the  elements  of  all  knowl- 
edge are  ideas  (by  which  is  meant  what  are  now 
commonly  called  notions  or  concepts),  and  that 
"  knowledge  [is]  but  the  perception  of  the  connec- 
tion and  agreement,  or  disagreement,  or  repugnancy 
of  any  of  our  ideas  "  (Essay,  b.  4,  c.  i). 

This  definition,  it  will  be  observed,  is  too  nar- 
row, as  it  excludes  the  knowledge  derived  directly 
from  the  perception  of  concrete  objects.  But  al- 
lowing for  this  defect  it  is  accurate  and  profound 
and  must  be  taken  as  the  foundation  of  all  science. 
In  the  beginning  it  seems  that  Locke  had  no 


APPENDIX  NOTES  259 

conception,  or  at  least  a  very  inadequate  conception 
of  the  intimate  connection  between  language  and 
thought,  and  of  the  indispensability  of  the  former 
as  an  instrument  of  thought.  But  as  he  proceeded 
he  seems  gradually  to  have  realized  this  great  truth, 
—  which  is  treated  of  in  his  third  book;  and  upon 
the  conclusions  thus  reached  is  based  his  theory  of 
knowledge  and  his  general  philosophy  as  developed 
in  his  fourth  book,  and  as  generalized  in  the  conclu- 
ding chapter,  to  which  we  have  referred.  His  theory 
of  knowledge,  therefore,  is  to  be  regarded  as  based 
to  a  great  extent  expressly,  and  otherwise  implicitly, 
upon  the  notion  that  all  knowledge  beyond  that 
coming  from  experience  consists  in  the  perception 
of  the  agreement,  or  disagreement,  of  our  ideas,  or 
notions;  and  hence  that  all  reasoning  must  consist 
in  the  comparison  of  notions  or  concepts;  that 
practically  this  can  be  effected  only  by  means  of 
the  names  of  the  concepts  or  notions;  and  hence 
that  Logic  must  consist  in  Analysis  and  Synthesis 
of  names  or  terms;  which  is  the  theory  of  this 
work.  (See  observation  of  Home  Tooke,  Appen- 
dix A.) 


INDEX 

Abstract  and  concrete  terms,  37 

Accent,  fallacy  of,  203 

Accident  and  genus  distinguished,  49 

Accident  and  secunJum  quid,  relation  between,  2IO 

Accident,  fallacy  of,  207,  208 

Adjectives  regarded  as  substantives,  36 

Amphiboly,  201 

Analysis  and  synthesis,  logical  and  physical,  distinguished,  108 

Analysis,  use  of,  116 

Analytical  processes,  42 

Apodictic,  23,  70 

Apprehension,  41 

A  priori,  and  empirical  notions,  71 

Arguing  in  circle,  160 

Aristotle,  his  dictum,  76  ;  his  classification  of  fallacies,  197 

Bain,  an  opinion  of,  83 
Burden  of  proof,  164 

Canons  of  the  several  figures  of  syllogism,  100 
Categories  and  predicables  distinguished,  66 
Classification,  division  and,  44 
Collective  and  distributive  interpretation,  60 
Commonplace  and  original  thought  distinguished,  112 
Commonplaces,  156 

The  numbers  refer  to  sections. 
26l 


262  INDEX 

Common  terms,  singular  and,  35 

Composition  and  division,  fallacy  of,  202 

Concept  defined,  30 

Concrete  terms,  abstract  and,  37 

Confusion,  fallacy  of,  139 

Connotation  and  denotation  of  terms,  32 

Consequent,  fallacy  of  the,  212 

Consequentis,  F.,  212 

Contradiction,  the  law  of,  125 

Contradictory,  substitution  of,  80 

Contraposition,  conversion  by,  So 

Conversion  by  intension,  58 

Conversion  of  propositions,  54,  70,  91 

Conversions,  material  and  formal,  distinguished,  92 

Copula,  the,  55 

Criticism,  115 

Definition,  vocal,  43  ;  nominal  or  real,  48 

Denotation  and  connotation  of  terms,  32 

Dialectic,  23,  70 

Dichotomy,  47 

Dictum,  Aristotle's,  76  ;  forms  of,  99  ;  applicable  to  all  fig- 
ures, 100,  101  ;  and  to  singular  and  other  equational 
propositions,  102  ;  proposed  amendments  of,  103 

Division,  46 

Division  and  classification,  44 

Enthymemes,  105 

Equational  theory  of  predication,  56 

Equivalence  of  terms,  78 

Equivocation,  fallacy  of,  127,  191,  201 

Essence  of  term,  49 

Euclid,  his  fifth  proposition  reduced  to  syllogisms,  84 

Excluded  middle,  the  law  of,  125 

Extension  and  intension  of  terms,  34 

The  numbers  refer  to  sections. 


INDEX  263 

Fallacies,  classification  of,  129 ;  definition  of,  128  ;  observa- 
tions on,  132  ;  extra  dictionein,  206  ;  in  dictione  (equivo- 
cation), 201  ;  of  inference,  131;  of  judgment,  130;  of 
the  syllogism,  104,  124 

False  definition,  fallacy  of,  126,  144 

Figiirce  dictio nis,  F.,  204 

Figure  of  speech,  fallacy  of,  204 

Figures  of  the  syllogism,  95 

Formal  and  material  conversions,  92 

Formal  and  material  relations  of  terms,  67 

Formal  fallacies,  104 

Genus  and  accident,  49 
Genus  and  species,  45 
Genus  of  term,  49 


Ilomonymy,  201 

Hypothesis,  argument  from,  165  « 

Hysteron  proteron,  160 


Identity,  the  law  of,  125 

Ignoratio  elenchi,  fallacy  of,  126,  169 

Illicit  assumption  of  premises  (petitio  principit),   154 ;  tests 

of,  162 

Illicit  conversions,  127,  183 
Illicit  generalization,  155 
Illicit  substitution,  fallacy  of,  127,  187 
Immediate  inferences,  80 
Inference,  rules  of,  77,  123,  127 
Inferences,  immediate,  80 
Infinitation,  80 
Instance,  or  extreme  case,  163 
Intension  and  extension  of  terms,  34 
Intensive  conversion,  58 
Intensive  theory  of  predication,  58 
Intuitive  propositions  or  judgments,  18,  19 

The  numbers  refer  to  sections. 


264  INDEX 

Invention,  113 

Irrelevant  conclusion,  fallacy  of,  126,  169,  173 

Judgment,  defined,  19  ;  rules  of,  126 
Judgments  and  assumptions  distinguished,  68 

Knowledge  defined,  i,  2,  5 

Language,  as  record  of  human  thought,  4  ;  as  source  of 
opinion,  3 

Laws  of  thought,  the,  125  :  the  law  of  identity,  125  ;  the 
law  of  contradiction,  125  ;  the  law  of  excluded  middle, 
125 

Legal  maxims,  158 

Logic,  definition  of,  14,  16  ;  the  traditional,  85  ;  decadence 
of  the  age  in,  n  ;  method  of,  in  ;  the  morality  of  in- 
tellect, 27  ;  the  art  of  right  reasoning,  26  ;  the  ultimate 
criterion  of  truth,  10  ;  as  the  doctrine  of  signs,  no 

Logical  processes,  107,  112 

Logical  term,  elements  of  the,  31 

Material  and  formal  conversions,  92 
Material  and  formal  relations  of  terms,  67 
Mathematical  reasoning,  82 
Meaning  and  signification  of  terms,  33 
Method  of  logic,  in 
Mistaking  the  issue,  169,  170 
Moods  of  the  syllogism,  94 

Moral  sciences,  distinguished,  6  ;  decadence  of  the  age  in  the, 
ii 

Name  defined,  28 

Negative  terms,  positive  and,  39 

Nominal  or  real  definition,  48 

Non  causa  pro  causa,  fallacy  of,  159 

Nonsense,  fallacy  of,  126,  134,  138 

Notion  defined,  30 

The  numbers  refer  to  sections. 


INDEX  265 

Onus  probandi,  164 

Opinion,  its  modes  of  generation,  7  ;  language  as  source  of,  3 

Opposition  of  propositions,  89 

Original  and  commonplace  thought  distinguished,  112 

Petltio  prin  fipii,  fallacy  of,  126 
Plurium  inter  rogationum,  F.,  171 

Popular  proverbs,  157 

Positive  and  negative  terms,  39 

Post  hoc  ergo  propter  hoc,  159 

Predicahles,  definition  and  division  of,  61  ;  and  categories  dis- 
tinguished, 66 

Predication,  theories  of,  55,  60 

Property  and  specific  difference  distinguished,  49 

Proposition,  defined,  22,  50  ;  the  grammatical,  51  ;  the  logi- 
cal, 52  ;  interpretation  of  the  logical,  53  ;  the  traditional 
doctrine  of  the,  86 

Propositions,  conversions  of,  54,  91  ;  kinds  of  :  intuitive,  18, 
20  ;  quasi-intuitive,  20  ;  inferred,  21 

Proverbs,  popular,  157 

Quality  of  propositions,  86 
Quantification  of  the  predicate,  57 
Quantity  of  propositions,  87 
Quasi-thing  defined,  29 
Question-begging  terms,  161 

Ratiocination,  defined,  14,  15  ;  not  merely  hypothetical,  72 

Real  things  defined,  29 

Reasoning,  defined,  14  ;  supposed  distinction  between  quali- 
tative and  quantitative,  82 

Rcductio,  ad  absurdum,  165  ;  ad  impossibile,  165  « 

Reduction  of  syllogisms,  96 

Relations  of  terms,  immediate  ;  intuitive  relations  or  judg- 
ments, 18,  19  ;  quasi-intuitive,  or  assumptions,  20 ;  in- 
ferred relations  or  syllogisms,  21 

The  numbers  refer  to  sections. 


266  INDEX 

Right  reasoning  defined,  25 

Rules,  of  logic,  twofold  division  of,  121  ;  of  inference,  77, 
123,  127  ;  of  judgment,  122,  126  ;  of  the  syllogism,  104 

Secundum  quid,  fallacy  of,  209 

Semeidtike,  or  the  doctrine  of  signs,  no 

Several  questions,  fallacy  of,  171 

Significates  of  terms,  33 

Signification  and  meaning  of  terms,  33 

Simple  apprehension,  41 

Singular  and  common  terms,  35 

Sorites,  106 

Species,  genus  and,  45 

Specific  difference,  49 

Substitution,  the  principle  of,  77  ;  formal  and  material,  Si  ; 
of  contradictory,  80 

Syllogism,  analysis  of,  74  ;  definition  of,  22,  75  ;  elements  of, 
73  ;  moods  and  figures  of,  94,  95  ;  principle  of,  76  ;  re- 
duction of,  96  ;  rules  of,  104  ;  the  traditional  doctrine  of, 
93 

Term,  defined,  28  ;  kinds  of,  35 

Terminal  relations,  generally,  64  ;  kinds  of,  17,  65 

Tests  of  illicit  assumption,  162 

Thing  defined,  29 

Thought  defined,  30 

Traditional  doctrine  of  fallacies,  197 

Traditional  theory  of  predication,  59 

Universe  of  the  proposition,  40 
Vocal  definition,  43 

Word  defined,  28 

The  numbers  refer  to  sections. 


UC  SOUTHERN  REGIONAL  LIBRARY  FACILITY 


A    001  401  248    8 


CALIFORNIA 


LIBRARY, 

ANGELES,  CALIF. 


